{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Continuous Random Variables**\n",
    "\n",
    "A random variable *X* is called **continuous** if there is a nonnegative function $f_X\\hspace{1pt}$, called the **probability density function** (or PDF) such that\n",
    "\n",
    "$$P\\left(X\\in B\\right) = \\int_B f_X\\left(x\\right)dx$$\n",
    "\n",
    "for every subset *B* of the real line. The probability that the value of *X* falls within some interval is \n",
    "\n",
    "$$P\\left(a\\le X \\le b\\right) = \\int_a^b f_X\\left(x\\right)dx$$\n",
    "\n",
    "Finally, the normalization property must hold\n",
    "\n",
    "$$\\int_{-\\infty}^{\\infty} f_X\\left(x\\right)dx = 1$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Value**\n",
    "\n",
    "The expected value (or mean) of a continuous RV is defined by\n",
    "\n",
    "$$E\\left[X\\right] = \\int_{-\\infty}^{\\infty} x f_X\\left(x\\right)dx$$\n",
    "\n",
    "Note that the expected value is well-defined if $\\int_{-\\infty}^{\\infty} \\left|x\\right| f_X\\left(x\\right)dx$ is well defined. This is not the case, for example, for certain power law distributions. \n",
    "\n",
    "Likewise, any real-valued function, $Y=g\\left(X\\right)\\hspace{1pt}$, of a continuous RV *X*, is itself a RV (possibly discrete) whose expected value is\n",
    "\n",
    "$$E\\left[g\\left(X\\right)\\right] = \\int_{-\\infty}^{\\infty} g\\left(x\\right)f_X\\left(x\\right)dx$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Variance**\n",
    "\n",
    "The variance of a continuous RV, *X* is defined by\n",
    "\n",
    "$$var\\left(X\\right) = E\\left[(X-E\\left[X\\right])^2\\right] = \\int_{-\\infty}^{\\infty} \\left(x-E\\left[X\\right]\\right)^2 f_X\\left(x\\right)dx$$\n",
    "\n",
    "which is equivalent to\n",
    "\n",
    "$$var\\left(X\\right) = E\\left[X^2\\right] - \\left(E\\left[X\\right]\\right)^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Joint PDFs of Multiple Random Variables**\n",
    "\n",
    "Two random variables, *X*, and *Y* are **jointly continutuous** if there is a **joint PDF** $f_{X,Y}\\hspace{1pt}$ such that\n",
    "\n",
    "$$P\\left(\\left(X,Y\\right) \\in B\\right) = \\int \\int_{\\left(x,y\\right)\\in B} f_{X,Y}\\left(x,y\\right) dx dy$$\n",
    "\n",
    "for every subset *B* of the $R^2\\hspace{1pt}$ and the normalization property holds\n",
    "\n",
    "$$\\int_{-\\infty}^{\\infty}\\int_{-\\infty}^{\\infty} f_{X,Y}\\left(x,y\\right) dx dy = 1$$\n",
    "\n",
    "One can view $f_{X,Y}$ as the probability per unit area at $\\left(x,y\\right)$.\n",
    "\n",
    "The **marginal** PDF of *X* (and similarly for *Y*) is\n",
    "\n",
    "$$f_X\\left(x\\right) = \\int_{-\\infty}^{\\infty} f_{X,Y}\\left(x,y\\right) dy$$\n",
    "\n",
    "Note that calculating the marginal PDF, $f_X\\left(x\\right)\\hspace{1pt}$ typically involves finding a parametric equation, $x=g\\left(y\\right)\\hspace{1pt}$ so that\n",
    "\n",
    "$$f_X\\left(x\\right) = \\int_{-\\infty}^{g\\left(x\\right)} f_{X,Y}\\left(x,y\\right)dy$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example: Buffon's Needle**\n",
    "\n",
    "Consider a surface ruled with parallel lines separated by a distance *d* and a needle of length $l \\lt d\\hspace{1pt}$. Suppose the needle is randomly placed on the surface. The probability that the needle will intersect a line is derived as follows. Let *X* by the vertical distance from the *midpoint of the needle* to the nearest line and let $0\\le\\Theta\\le\\pi/2\\hspace{2pt}$ by the acute angle formed by the needle (extended infinitely) and the lines. Assuming the placement is uniformly random the **joint PDF** is\n",
    "\n",
    "$$f_{X,\\Theta}\\left(x,\\theta\\right) = \\left\\{ \\begin{eqnarray} 4/\\left(\\pi d\\right) &,& \\quad \\mbox{if} \\hspace{2pt} x\\in\n",
    "\\left[0,d/2\\right] \\hspace{2pt} \\theta \\in \\left[0,\\pi/2\\right] \\cr\n",
    "0 &,& \\quad\\mbox{otherwise}\\end{eqnarray}\\right.$$\n",
    "\n",
    "The needle will intersect a line iff $X\\le \\frac{l}{2}\\sin\\Theta\\hspace{2pt}$, so the probability of intersection is\n",
    "\n",
    "$$\\begin{eqnarray} P\\left(X\\le (l/2)\\sin\\Theta\\right)&=& \n",
    "\\int\\int_{x\\le(l/2)\\sin\\theta}f_{X,\\Theta}\\left(x,\\theta\\right)dxd\\theta \\cr \n",
    "&=& \\frac{4}{\\pi d} \\int_0^{\\pi/2}\\int_0^{(l/2)\\sin\\theta}dx d\\theta \\cr\n",
    "&=&\\frac{2l}{\\pi d}\\end{eqnarray}$$\n",
    "\n",
    "Note that this example, [rather famously](http://en.wikipedia.org/wiki/Buffon's_needle#Estimating_.CF.80), provide an experimental method for calculating $\\pi\\hspace{1pt}$. By conducting the above experiment enough times we can approximate $\\pi\\hspace{1pt}$ as\n",
    "\n",
    "$$\\pi = \\frac{2l}{d}\\frac{1}{P_{exp}\\left(X\\le (l/2)\\sin\\Theta\\right)}$$\n",
    "\n",
    "where $P_{exp}\\left(X\\le (l/2)\\sin\\Theta\\right)\\hspace{1pt}$ is the observed value. If we choose $d=2l\\hspace{1pt}$ then the observed probability will equal the inverse of the estimate for $\\pi\\hspace{1pt}$. We simulate this below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theoretical Probability = 0.318309886184\n",
      "Observed Probability = 0.31758\n",
      "Final estimate of pi = 3.14881289754\n",
      "Python pi = 3.14159265359\n"
     ]
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAW8AAAEECAYAAADnD7WNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAHn1JREFUeJzt3Xd4VFX+BvB3ICBSBaRJC72XIEiRmIAKKATIqhiw8AgI\n",
       "sgssuK64lh/RZUHWtlRRKcuCFAuCYEgEZYAA0lWkSBGkSseYACHJnN8fX8ebhGQKuTP3nsn7eR6e\n",
       "aXfunByGN4dzT3EopRSIiEgrRawuABER+Y/hTUSkIYY3EZGGGN5ERBpieBMRaYjhTUSkoTBvB4SH\n",
       "h6Ns2bIoWrQoihUrhq1btwajXERE5IHX8HY4HHA6nahQoUIwykNERD7wqduE83iIiOzF4W2GZd26\n",
       "dVGuXDkULVoUw4YNw9NPP53zBA5HQAtIRBSKCtwoVl6cOnVKKaXU2bNnVatWrdT69etzvO7DKfwy\n",
       "btw4U4/P73Vfn/f02NuxBeXP+Xw5Nlh1YXY9+HtO1oV/x7IuvB9jdl2YkZtF4+Pj4z2Fe5kyZQAA\n",
       "pUqVwpkzZ3Du3Dl06tTpj9dfffVVeDmF38LDw009Pr/XfX3e0+Ps951OJ6Kjoz2WxV/+1IUvxwaj\n",
       "LgJRD3l9dkGPZV14P4Z14f/zvtSFKbnpKdnT0tJUSkqKUkqp1NRU1alTJ5WUlJTjGC+nKFQC0bLQ\n",
       "EevBwLowsC4MZuSmx9EmZ86cQWxsLAAgMzMTjz32GLp161aw3xYhLBCtCh2xHgysCwPrwlxeL1h6\n",
       "PYHDwdEoRER+MCM3OcOSiEhDDG8iIg0xvImINMTwJiLSEMObiEhDDG8iIg0xvImINMTwJiLSEMOb\n",
       "iEhDDG8iIg0xvImINMTwJiLSEMObiEhDDG8iIg0xvImINMTwJiLSEMObiEhDDG8iIg0xvImINMTw\n",
       "JiLSEMObiEhDDG8iIg0xvImINMTwJiLSEMObiEhDDG8iIg0xvImINMTwJiLSEMObiEhDDG8iIg0x\n",
       "vImINMTwJiLSEMObiEhDDG8iIg0xvImINORTeGdlZSEiIgIxMTGBLg8REfnAp/CePHkymjZtCofD\n",
       "EejyEBGRD7yG94kTJ5CQkIAhQ4ZAKRWMMhERkRdh3g4YM2YM3njjDaSkpOR7THx8/B/3o6OjER0d\n",
       "bUbZiIhCgtPphNPpNPWcDuWhOb1y5UqsWrUK06dPh9PpxFtvvYUVK1bkPIHDwRY5EZEfzMhNj90m\n",
       "mzZtwueff446deqgf//++Prrr/Hkk08W6AOJiKjgPLa8s1u3bh3efPNNtryJiAoo4C3vvD6QiIis\n",
       "53PLO98TsOVNROSXoLe8iYjIHhjeREQaYngTEWmI4U1EpCGGNxGRhhjeREQaYngTEWmI4U1EpCGG\n",
       "NxGRhhjeREQaYngTEWmI4U1EpCGGNxGRhhjeREQaYngTEWmI4U1EpCGGNxGRhhjeZFu9ewN79lhd\n",
       "CiJ7YniTLSkFrFgBTJlidUmI7Il7WJItHTsG1K4t9/n1olDDPSwpZO3aZXUJiOyN4U22c/480Lcv\n",
       "8OST8nj9emvLQ2RHDG+ynR075PbBB+U2JcW6shDZFcObbGf3brlt2hSIiwNOn/btfSdPAklJgSsX\n",
       "kZ3wgiXZzoABQKtWwNixgMMhz61aJaNPXnsNqFjxxvdcvw7ccovcnz0bGDQoeOUl8hcvWFLQLVsG\n",
       "bNlizrlOnJBw/vRTud2zB5g5E1i0yOgy+dvf5PaBB4AZM4DIyLzP5Q5uABg8GDh1yvNnL10KvPEG\n",
       "u2RIX2x5k1+6dwfuvhv4v/8r+Lncreq8ZGQAYWHShdKyZc7XNm4EOnUyHp8+Ddxxx43n8PS1LF8e\n",
       "uHzZ+3G6+eAD+ftp2tTqkpAnbHlTUCklFxN97YP2ZMMGz6+HhcltpUrGc+4Qv/tuuR0xArj9diO4\n",
       "L14Erlwxjk9Lu/G8zz4LvPyyEdyAdLmEgvnzgaFDgWbNZJx8errVJaJAYsubfHb0KFCnjgzj++yz\n",
       "gp3LU6v74EGgfn25rxTw1VdAVBTgdALdusnzhw4Zx7i5v4aRkUByMnD4MFC3rvF6RgZQvPiNn7dk\n",
       "CdCv303/KLagFFAkj6ZYZiZQtGje7/nlF6By5bzfR4HFljcF1Y4d0hIuaMs7NdW4/9pr0hWTliYX\n",
       "KH/+OWcoOxzAffcBxYoB998PnDsnz+cO7ogI4/6GDcBddwFnzwK//QZ8/bU8nzu4XS65/eabgv08\n",
       "Zrt0CbjzTv/eM2OG3J4/n/P5sDCpQ4dD6qR0aeNxtWoS7O7H7l+o2f9+yL4Y3uSzrVuBmBhpsd2s\n",
       "yZOBhAS5/9RTQJ8+wJgxQMmSwOuvA7VqeX7/7bfnfNykibQ6d+7M+XyRIsAPPwBlywL33ist8ewm\n",
       "TJCwKlIEeOcdoGbNvD9v/Xr5BRAMSkmZKlSQn2ffPu/vSUgAbrtNupBKlpSROErJn+eey3nstm15\n",
       "dyVl53AAZcoYvyTJxlQBmXAK0kRUlFLLlyt1yy1KuVz+v9/lklgJC1PqL3+5+XJs365Ujx5KDRum\n",
       "1BNP5H2MEWE5/2Rlye3q1XLc/v3Ga7lduGC8du3azZfXm0uX8i9vXuVy12PuPwcO3HhsVpZS06cr\n",
       "tWKFHNOxozx/8aKc59o1peLj5X5ERM7zvf123uU9dkypLVuUunJF7ptpxw5zz2dXZuQmw5t8kpmp\n",
       "VOnS8o++XDm5zUu5ckp17apUWtqNr/38sxEM//1vwct08aJSp07l/doLL8jnFClifObo0Xkf6349\n",
       "d5mzB9kDD+T93qysG3+RpaYqtWePUocO5V/2+fOV6tVLqfr15db9ObffLq8/8UTOz790Salz55Sq\n",
       "Vi3n8yVKKPX000r9+GP+n+UPl0upUaOM8zduLLcREUo1aZL/L5hvvrnxl4onHTp4/oWV/U+pUkqN\n",
       "HKnURx8pNWOGOT9nQbhcSo0Zo9Sf/qTU1as3/tyvvaZUenr+792zx5zcNOeCZbt2ZvwngGzsylW5\n",
       "SNiyBfD9bqBBfeDWW3Mek+UyprY3bw6UzPb6hYuAA8Chw/K4RfMb32+mq9dkmKHDYVzIbNdOypCX\n",
       "b78DGjcGSvw+XlwpYNv2nMe0aAHcWiLnc1u3yc8RXhsoWUrOv32H8fpd2f5pKADKBezbf2P3ReXK\n",
       "co7sx/76K3DgQN7lLVYMaN06/5/HDFu35f9a7VrSN5/iY5dSmdLAb6lAgwZyQTo/txQH0v0Y/XNn\n",
       "G/nepaUBriz5uzh7VlakdDjkM93dTxER3hc8cziARo2ArCwpZ6NGwI8/+l4eX7XHtgJfsDQnvM2a\n",
       "tUG2tXy5fPHj44Hhw4FBg4F2bY3XXS7g22+BZ4bL4ymTgQ4d5P7ly0C37kCXaKBqVWDRYmDzpvxH\n",
       "QZjlrvZyu9WHr+dd7YE2ETJJKPt7kzcA+/cDQ56Wxw5IsALAwg+BAY95Pu/HH0mg7N0LPD8252st\n",
       "mgO7f5D7X38lFxNz++mILBHgFtNLrgsMHOj9ZzLDuXPSp/7laqBWTfkFltu6dcAnnwBbtgLTp8v3\n",
       "4ocf5DuSn54PAi+9DIT58B04dAg4cRLIzJDPSvry5n8eMzRrCsyaJUE/e7b8Hf1rvDFqx+WSEUzv\n",
       "/Cfn+16NlwvIXbsCYZ3aF3yUXkGb7iacgjQwZIhS06bJ/bg4pRYsyPn64ME5/+s4d64873JJF4H7\n",
       "+cREpTIyglPm8eOV+vRT347N/l/9K1du/K9/x46+/zff/T5Pr5854/vPkZmpVEyMUiNG+P4eOzl8\n",
       "WK5TKKXUpk03d70kLxcvyrWTSZOUWrdOurCOHJF+/Nx/FxkZSn3/vfdzuq8DuLtDkpPNK292ZuSm\n",
       "x5b3tWvXEBUVhfT0dFy/fh19+vTBxIkTcxzDcd6FQ8uWwJw5QNu2wDPPAO+9J5NA3MPvypSRIWYz\n",
       "Zsh/U6tUAV56CZg2DRg50jjPhQsymsJuVq6UkTQ7dwJt2shzLpcxfO6bb4COHW9837Rp0jL+6ScZ\n",
       "lVKjhtRJeDjQvz+weLFx7KhRwMMPA507ex7nTqHPjNwM8/RiiRIlsHbtWpQsWRKZmZno3LkzkpOT\n",
       "0blz5wJ9KOljxw4ZGnj4sDHD8eRJuT11SkIKMMYG33uvTAxx9zNu3iy3Tz0FzJ1rz+AGjMB230ZF\n",
       "5QzYDh2kHXftmqxcWKYMUKoU0P737pW8FstatEj+rFsHnDmj/0Qgshef+7yvXLmCqKgozJs3D02z\n",
       "LZzAlndoGzpUZjhWrmwE8ZdfysSa9etlNuPZs9LSBuRCz7JlwEMPAeXKyUU3QBahUkpapnaVPaz5\n",
       "laZACnjLGwBcLhfatGmDw4cPY/jw4TmC2y0+Pv6P+9HR0YiOji5Qocg+vvlGugRiYoznunWTVuTx\n",
       "4/J482agRw9ZthUAqleXW3dwr11rPGdnWVlyEfXYMatLQqHG6XTC6XSaek6fW96//vorunfvjtdf\n",
       "fz1HOLPlHbpSUmSkgVLAwoXSh+v23HMyVX7sWPlTujTwyivy2vHjOWdK8utBlFNQ1zYpV64cevbs\n",
       "ie3bt3s/mELCtm3G0qLuvl23mjWNlvemTTmXaK1Wzbg/YkRgy0hUWHkM7/Pnz+Py72tnXr16FatX\n",
       "r0ZE9hWASEs7dnieKOG2aZNsijBzpqwmmJ07vK9fl/Hfd91lvBYWZgzUmjrV3LITkfAY3qdPn0bX\n",
       "rl3RunVrtG/fHjExMbj33nuDVTYyQVaWBO+lS8Zzr70GLFjg/b3JyTKsbdiwG4e2ucN71y6ZNVem\n",
       "jLnlJiLPPF6wbNGiBXbmXq6NtPLdd7IO9+HDMkbb5ZJQLlvW8/syM+Vi5Ycf5v16zZoygiR3lwkR\n",
       "BQeXhA1x7h1rDh+WQN6/X1rhR454ft/u3TJCJPcSrG6VK8sFza+/ZngTWcHrUEHS2/r1cgHxxRdl\n",
       "skjr1kB0tIS4J+4uk/wUKSLhnpQETJliapGJyAdseYcgp1PGZSslLe8BA2Ss9r598vjRR2W/x6tX\n",
       "8z/Hxo2ewxuQ2ZUVKxqzLIkoeBjeISgxUS4kHjgAlCghU70B6TpJTpbHtWrJlmO5/fijtNY3bDA2\n",
       "+s1PeLh0mXCdDqLgY7dJCHI6Zf2R1atl+nqjRrIR7/HjcqGyUSMZgfLTT7KGdXbvvSfdKy5Xzs17\n",
       "89KrF4ObyCpseYeY1FRZS7lWLeB//5PwbthQukxq1jRWtKtTR6a4f/xxzvc7nbKyni8r38XGyk7y\n",
       "RBR8DO8Q4b4AuXGj7DzerJnMkLznHnm+eHFpSbv7sevWld1Hsu+jcfmycR4uHElkb+w2CQEnTkhY\n",
       "p6RIl0dUlAwHrFhRdld3mzjRuLjo3oIs+xZP7n7uXbsY3kR2x5Z3CHA6pY/6wAG5Hx0tsx4jI3N2\n",
       "fbRta4zbjo0Fnngi5x6J69bJezdvNta1JiJ7Yss7BDidMu56507g++9l44D27WVIYH5q1AA++EDW\n",
       "3M7IkA1tnU7gP/+R4CciezNnA2Ku+WmpevVkY9jz56Wl7Z5V6Yu6dWWiTeXKMunmwgXgllsCV1Yi\n",
       "CvKSsGRPx47J3ol/+pNcrHSP6fZVw4by55VXpLXO4CbSA8NbQwcPGkP81qyRfSPd47X93cSoalW5\n",
       "nTvX/+AnIuswvDU0bx7w1ltyf80a4L77ZOJNuXJ573DuibulnZrqf/ATkXXY562hDh1kIs6vvwJ3\n",
       "3AFs3QrUri3jtkuV8u9cKSmy7OuYMTLOu0SJwJSZiAxB2YCY7OXyZWDPHtn84PPPZbp77drymr/B\n",
       "Dcj7BwyQoYYMbiJ9sOWtmWXLgBkzZGjfb7/J5Jx337W6VETkD442KYRWrwbuv1+GBm7YIP3dRFT4\n",
       "MLw1ohSwahXQo4eEt8MBdOlidamIyArs89bIwYOyW3vz5kDp0kD//kCFClaXioiswD5vjUyeLHtL\n",
       "zppldUmIqCDY513IJCYCDzxgdSmIyA7Y8tbE1auy/sjx48Btt1ldGiIqCLa8C5F164CICAY3EQmG\n",
       "tyZWrWKXCREZGN6acA8RJCICGN5aOHhQFo5q1crqkhCRXTC8NbB8OdC7t+yWQ0QEMLy1sGwZ0KeP\n",
       "1aUgIjtheNvQ7t3A1Kly/+xZWf61a1dry0RE9sLwtqH33gP+9S9ZpnXFCqBbN25PRkQ5MbxtxuWS\n",
       "bpL0dGmBL18O9O1rdamIyG4Y3jazfbtstDBgAPDZZ4DTCTz4oNWlIiK74aqCNvPZZ0BsrOzk/vjj\n",
       "suUZZ1USUW4MbxtRCli6FFiwQDYUvnqVo0yIKG8Mbxv57jsgIwNo21Y2WpgwAejXz+pSEZEdeezz\n",
       "Pn78OLp06YJmzZqhefPmmDJlSrDKVSgtWgTExUlwA8Dzz8tKgkREuXlcEvaXX37BL7/8gtatWyM1\n",
       "NRV33nknli1bhiZNmhgn4JKwplAKCA+XoYEtW1pdGiIKpIAvCVu1alW0bt0aAFC6dGk0adIEp06d\n",
       "KtAHUt42bwZKlZK9KYmIvPG5z/vo0aPYtWsX2rdvf8NrI0bE4/bb5X50dDSio6PNKl/IWL9ednt/\n",
       "6SV5fPgw8OabwLvvyuPFi2VPSneXCRGFDqfTCafTaeo5fdpJJzU1FdHR0Xj55ZfRN9eMEYfDgdq1\n",
       "FTZuBKpXN7VsISU2FvjyS+D0aaBsWQnxCROAPXtkZEmNGrLhQsOGVpeUiAItKDvpZGRk4KGHHsLj\n",
       "jz9+Q3C7/fnPstb0pUsFKkvIunABWLsW6NQJWLJEZlF++KFsrvDf/8pEnDvuYHATke88dpsopTB4\n",
       "8GA0bdoUo0ePzve4v/9dWpR9+gBJScCtt5peTq0tWSJB/dhjsmZJ48Yyi/Ltt4EuXYBz56TLhIjI\n",
       "Vx67TZKTk3HPPfegZcuWcPzeGTtx4kT0yLali7v573LJjMCrV4FPPgGKFg184XXRoQMwbhxw//1A\n",
       "7dpAgwYS5mPHAh07Alu3AkeOALVqWV1SIgoGM7pNTN09/vp1oGdPoG5dYOZMXnwDgAMHgHvuAU6c\n",
       "AMLCgBdfBCZOBI4dA2rWBObOBf73P+lWIaLCwXbhDQC//SZdAb16AfHxBSpbSHjlFdnC7J135PGx\n",
       "Y8Ds2cCrrxrHpKdzyVeiwsSW4Q3IBgJ33w387W/AM88UqHxay8qSiTcrV3L/SSIymBHeAVnbpHJl\n",
       "IDFRuguqVJFhcoVRYqKMImFwE5HZArYwVb16MtW7Rw+gYkUJ8sLm/feBoUOtLgURhaKAdJtkt2aN\n",
       "DJFbs6ZwTf0+eVJ+3mPHgNKlrS4NEdlJUCbpFNR99wGTJ8tuMD//HOhPs4+5c2U5VwY3EQVCUNbz\n",
       "jouTi5jduwPJyfhjHZRQ5XIBs2bJxgpERIEQtD0sR42SC5e9egFpacH6VGskJsovqDZtrC4JEYWq\n",
       "gPd5Z6cUMGiQtMKXLQOKFSvIJ9tX9+6ygfDAgVaXhIjsyLbjvD3JyAD69gUqVZJ+4VCbhbl3L9C1\n",
       "q/Tvc+INEeVFiwuWuRUrBnz0EbB/v0wVDzVTpsjEJAY3EQVS0FvebhcuAJ07S9D99a8FKYF9XLwo\n",
       "49v37QOqVrW6NERkV7adYemLihVl+di775ZZmHFxVpXEPLNmATExDG4iCjzLWt5uu3fLWPAPP5Rb\n",
       "XWVkAPXry/DAO++0ujREZGda9nnn1qIF8PHHMjpj506rS3PzFi6U8GZwE1EwWN7ydvvsM+Avf5FN\n",
       "euvVK/DpgiorC2jWDJgxQ0aaEBF5onWfd26xscYszFWrZLcZXSxdCpQvL+uYExEFg23CGwCGDZOp\n",
       "5R07As8+Czz3HFC8uNWl8kwp2Zdy/PjQG7NORPZleZ93bsOHA9u3Axs3Sv/x5s1Wl8izhAS57dnT\n",
       "2nIQUeFimz7v3JSSC5mjR8uMzIkTgXLlTP+YAlFKhjqOHi0rCBIR+SIkRpvkx+GQQNyzx7gg+Omn\n",
       "Eph2kZgIXLoEPPSQ1SUhosLGti3v3JKTZVeaBg2AadNk53UruVxARIRsJNy3r7VlISK9hHTLO7fO\n",
       "nYFdu6QfPCJC1hDJyrKuPAsXAqVKAX36WFcGIiq8tGl5Z/fjjzIy5coV2SeydevAfZZS8ksiLNu4\n",
       "nPR0oHFjYN68wrk3JxEVTKFqeWfXqBGwdq0satWtm/Q5JycHpj980iSgRg3gvfeAzEx5buZM6YNn\n",
       "cBORVbRseWeXliYt4HfekYkyzz4rYW7GRg8//yzdNLNmAVOnAqdOAePGySqIhW1DZSIyj5abMQRK\n",
       "VhbwxRfA228DP/0EjBwJPP00cNttN3/O2FgJ75dfllZ9YiLw/PNAu3bAnDnmlZ2ICheGdz527JCW\n",
       "eEIC8MQTMkqlWTP/zpGQIC3s3buBEiWM55WSP0W07HAiIjtgeHtx4gQwfTowfz5QoYKsGf7oo94X\n",
       "vrp2DWjeXIYk9ugRnLISUeHB8PaRyyXT7Rcvllmb4eES5I88kvd48X/+E/j2W5kURERkNob3TcjM\n",
       "lJEqixfLDvbVq0vrukcPmep+6pT0ae/cCdSqZXVpiSgUMbwLKCsL2LZNLkQmJsrO7+XLyxDEf/zD\n",
       "6tIRUahieJvswgVZxbBbN/svRUtE+mJ4ExFpqNDOsCQiKuy8hvegQYNQpUoVtOB0QiIi2/Aa3k89\n",
       "9RQSExODURYiIvKR1/COjIxE+fLlg1EWIiLykSkbEMfHx/9xPzo6GtHR0WaclogoJDidTjidTlPP\n",
       "6dNok6NHjyImJga7d+++8QQcbUJE5BeONiEiKqQY3kREGvIa3v3790enTp1w4MAB1KxZE3Pnzg1G\n",
       "uYiIyAPOsCQiCjL2eRMRFVIMbyIiDTG8iYg0xPAmItIQw5uISEMMbyIiDTG8iYg0xPAmItIQw5uI\n",
       "SEMMbyIiDTG8iYg0xPAmItIQw5uISEMMbyIiDTG8iYg0xPAmItIQw5uISEMMbyIiDTG8iYg0xPAm\n",
       "ItIQw5uISEMMbyIiDTG8iYg0xPAmItIQw5uISEMMbyIiDTG8iYg0xPAmItIQw5uISEMMbyIiDTG8\n",
       "iYg0xPAmItIQw5uISEMMbyIiDTG8iYg0xPA2kdPptLoItsB6MLAuDKwLc3kN78TERDRu3BgNGjTA\n",
       "pEmTglEmbfHLKVgPBtaFgXVhLo/hnZWVhREjRiAxMRF79+7FokWLsG/fvoAWyN+/YG/H5/e6r897\n",
       "ehzoL6M/5/flWNaF92NYF/4/z7rw7bHZdeExvLdu3Yr69esjPDwcxYoVQ1xcHJYvX25qAXJjeOf/\n",
       "2QU9lnXh/RjWhf/Psy58e2x2XTiUUiq/Fz/55BMkJSXhgw8+AAAsWLAAW7ZswdSpU40TOBymFoiI\n",
       "qDDwEL0+CfP0oi/BXNACEBGR/zx2m1SvXh3Hjx//4/Hx48dRo0aNgBeKiIg88xjebdu2xcGDB3H0\n",
       "6FFcv34dS5YsQe/evYNVNiIiyofHbpOwsDBMmzYN3bt3R1ZWFgYPHowmTZoEq2xERJQPjxcsiYjI\n",
       "njjDkohIQ6aHd1paGgYOHIihQ4di4cKFZp9eK0eOHMGQIUPwyCOPWF0Uyy1fvhxDhw5FXFwcVq9e\n",
       "bXVxLLV//34MHz4c/fr1w+zZs60ujuXS0tLQrl07fPHFF1YXxVJOpxORkZEYPnw41q1b5/V408N7\n",
       "6dKl6NevH95//318/vnnZp9eK3Xq1MGsWbOsLoYt9OnTB++//z5mzpyJJUuWWF0cSzVu3Bjvvvsu\n",
       "Fi9ejKSkJKuLY7l///vfePTRR60uhuWKFCmCMmXKID093adRfT6F96BBg1ClShW0aNEix/N5rXty\n",
       "8uRJ1KxZEwBQtGhRf8tve/7URai7mboYP348RowYEcxiBoW/dbFixQr07NkTcXFxwS5qwPlTF6tX\n",
       "r0bTpk1RqVIlK4oacP7URWRkJBISEvD6669j3Lhx3k+ufLB+/Xq1c+dO1bx58z+ey8zMVPXq1VNH\n",
       "jhxR169fV61atVJ79+5V8+fPVytXrlRKKRUXF+fL6bXiT124Pfzww1YUNeD8qQuXy6Wef/55tWbN\n",
       "GgtLHDg3871QSqnevXsHu6gB509dvPTSS2r06NGqW7duqk+fPsrlcllYcvPdzPciPT3dp8zwOFTQ\n",
       "LTIyEkePHs3xXPZ1TwD8se7JqFGjMGLECHzxxRchOSbcn7qoUqUKXnzxRXz77beYNGkSxo4dG/wC\n",
       "B5A/dbFmzRp89dVXSElJwaFDhzBs2LDgFziA/KmLs2fPYunSpbh27Rq6dOkS/MIGmD91MX78eADA\n",
       "vHnzUKlSpZBbbsOfuti/fz+SkpJw+fJljBw50uu5fQrvvGTvHgGAGjVqYMuWLShZsiTmzJlzs6fV\n",
       "Un51UaFCBcycOdPCkgVffnUxdepUn76QoSS/uoiKikJUVJSFJQu+/OrCbeDAgVYUyxL51cULL7yA\n",
       "2NhYn89z0xcsQ+03ZEGwLgysCwPrwsC6MJhVFzcd3lz3xMC6MLAuDKwLA+vCYFZd3HR4c90TA+vC\n",
       "wLowsC4MrAuDaXXhyxXTuLg4Va1aNVW8eHFVo0YNNWfOHKWUUgkJCaphw4aqXr16asKECf5eiNUS\n",
       "68LAujCwLgysC0Mg64JrmxARaYhrmxARaYjhTUSkIYY3EZGGGN5ERBpieBMRaYjhTUSkIYY3EZGG\n",
       "GN5ERBpieBMRaej/Aexa5LWgqSRxAAAAAElFTkSuQmCC\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import uniform\n",
    "\n",
    "#choose d = 2l\n",
    "nl = 1 #needle length\n",
    "d = 2*nl\n",
    "\n",
    "#joint uniform random variable\n",
    "rv = uniform(loc=[0,0], scale=[d/2.0, math.pi/2.0])\n",
    "\n",
    "#number of times needle is randomly placed\n",
    "numSamples = 100000\n",
    "\n",
    "samples = rv.rvs(size=(numSamples,2))\n",
    "intersections = [samples[i][0]<=(nl/2.0)*math.sin(samples[i][1]) for i in range(numSamples)]\n",
    "piEst = [int(intersections[0])]\n",
    "for i in range(numSamples-1): piEst.append(piEst[i] + int(intersections[i+1]))\n",
    "piEst = [(i+1)/max(.1, float(piEst[i])) for i in range(numSamples)]\n",
    "\n",
    "print \"Theoretical Probability = {0}\".format(2*nl/math.pi/float(d))\n",
    "print \"Observed Probability = {0}\".format(numpy.sum(intersections)/float(numSamples))\n",
    "print \"Final estimate of pi = {0}\".format(piEst[numSamples-1])\n",
    "print \"Python pi = {0}\".format(pi)\n",
    "\n",
    "plot(piEst)\n",
    "plot([pi for i in range(numSamples)], 'r')\n",
    "pyplot.ylim(0,5)\n",
    "pyplot.xscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Joint CDF**\n",
    "\n",
    "If *X* and *Y* are two continuous RVs their joint CDF is\n",
    "\n",
    "$$F_{X,Y} = P\\left(X\\le x, Y\\le y\\right) = \\int_{-\\infty}^x \\int_{-\\infty}^y f_{X,Y}\\left(s,t\\right)dtds$$\n",
    "\n",
    "Conversely, the PDF can be obtained by differentiating:\n",
    "\n",
    "$$f_{X,Y}\\left(x,y\\right) = \\frac{\\partial^2 F_{X,Y}}{\\partial x \\partial y}\\left(x,y\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expectation**\n",
    "\n",
    "If *X* and *Y* are continuous RVs, then $Z=g\\left(X,Y\\right)\\hspace{1pt}$ is also a RV with exepcted value\n",
    "\n",
    "$$E\\left[g\\left(X,Y\\right)\\right] = \\int_{-\\infty}^{\\infty}\\int_{-\\infty}^{\\infty}g\\left(x,y\\right)f_{X,Y}\\left(x,y\\right)dxdy$$\n",
    "\n",
    "where again we note that, in general, $E\\left[g\\left(x,y\\right)\\right] \\ne g\\left(E\\left[X,Y\\right]\\right)\\hspace{1pt}$ although the equality does hold for linear functions of *X* and *Y*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Conditioning a Continuous RV on an Event**\n",
    "\n",
    "The **conditional PDF** of a continuous RV *X*, given and **event** *A* is defined ad\n",
    "\n",
    "$$P\\left(X\\in B \\vert A\\right) = \\int_B f_{X\\vert A} \\left(x\\right) dx$$\n",
    "\n",
    "In the **special case** where the conditioning event is of the form $\\left\\{X \\in A\\right\\}\\hspace{1pt}$ we have\n",
    "\n",
    "$$f_{X \\vert \\left\\{ X \\in A \\right\\} } =  \\left\\{ \\begin{eqnarray} \\frac{f_X\\left(x\\right)}{P\\left(X\\in A\\right)} &,& \\quad \\mbox{if} \\quad x\\in A \\cr\n",
    "0 &,& \\mbox{otherwise} \\end{eqnarray}\\right.$$\n",
    "\n",
    "An additional useful theorem is the following version of the *total probability theorem*. Let $A_1,\\ldots,A_n\\hspace{1pt}$ be *disjoint* events that form a partition of the sample space, then\n",
    "\n",
    "$$f_X\\left(x\\right) = \\sum_{i=1}^{n}P\\left(A_i\\right) f_{X\\vert A_i}\\left(x\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example: Exponential is Memoryless**\n",
    "\n",
    "Assume the time, *T*, until an atom undergoes a radio active decay is modelled as an exponential RV with paramter $\\lambda\\hspace{1pt}$. Now assume that at time *t* units the atom has *not yet decayed* corresponding to the event $A=\\left\\{T\\gt t\\right\\}\\hspace{1pt}$. Let *X* be the *additional* time until the atom decays. What is the conditional CDF of *X* given the event *A*? \n",
    "\n",
    "The analytical solution is given by\n",
    "\n",
    "$$\\begin{eqnarray}P\\left(X\\gt x \\vert A\\right) &=& P\\left(T\\gt t + x \\vert T\\gt t\\right) \\cr\n",
    "&=& \\frac{P\\left(\\left\\{T\\gt t+x\\right\\} \\cap \\left\\{T\\gt t \\right\\}\\right)}{P\\left(T\\gt t\\right)} \\cr\n",
    "&=& \\frac{e^{-\\lambda\\left(t+x\\right)}}{e^{-\\lambda t}} = e^{-\\lambda t} \\end{eqnarray}$$\n",
    "\n",
    "The result implies that if the waiting time for an event is modelled with an exponential RV and the event has not occurred after some time *t*, the **remaining** time to completion has the same CDF as when the wait started, that is there is no memory of past waiting time. Further, we know that the PDF is equal to the derivative of the CDF so the PDF is also the same.\n",
    "\n",
    "We simulate an example below. We will take many samples from an exponential RV. For any values that are greater than the mean, we will consider the additional wait time beyond the mean and calculate the PDF and CDF for those values. Note that if the original RV is less than or equal to the mean we will not have a realization of the additional wait time. Note we will calculate the CDF of the observed data using [cumulative frequency analysis](http://en.wikipedia.org/wiki/Cumulative_frequency_analysis). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x106f07e90>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAABC8AAAG0CAYAAAASKA0aAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4VfXhx/H3uSM3e4dsCBAlUaaAgEjFiRNHtVURrQMt\n",
       "lbpt62gZtfpDq3ZYq61ailrEDSJGRI1aBCKgAoKMhJAdssfNuOv8/kgbiYMCAucGPq/n4XnuN+ec\n",
       "m8+5SO7Nx+/5HsM0TRMRERERERERkSBlszqAiIiIiIiIiMieqLwQERERERERkaCm8kJERERERERE\n",
       "gprKCxEREREREREJaiovRERERERERCSoqbwQERERERERkaCm8kLkCJSVlUV4eDhRUVGkpKRw9dVX\n",
       "43a7mThxImFhYURHRxMTE8OoUaOYO3cuHo+n+9hZs2bhdDqJiorq/vP73//ewrMRERGRI8W//vUv\n",
       "Ro0aRVRUFGlpaZx99tmsWLGi+/NJdHQ00dHRDBo0iJ///OdUVVV1H5ufn4/NZuvxGeb888+38GxE\n",
       "ZF+ovBA5AhmGwZIlS2hpaWHdunWsWbOG++67D8Mw+Mtf/kJzczNVVVU8/PDDvPDCC5x99tk9jr3s\n",
       "sstoaWnp/nPHHXdYeDYiIiJyJHjkkUe49dZbuffee9m1axelpaXceOONLF68uPvzSXNzMw0NDbz2\n",
       "2mtUVVUxcuTIHgVGenp6j88wixYtsvCMRGRfqLwQOcKlpaVx1llnsXHjRgBM0wQgLCyMk046icWL\n",
       "F7Ny5UrefPPN7u3/3UdERETkUGhqamLmzJk8/vjjXHDBBYSFhWG32znnnHOYO3duj88ndrudY445\n",
       "hoULF5KUlMTDDz9scXoRORBUXogcof77Bl9aWsrSpUs57rjjvnW/zMxMRo0axUcffXQo44mIiIh0\n",
       "W7lyJR0dHVx44YV7fYzNZuP888/XZxiRw4TKC5EjkGmaXHDBBcTFxTFhwgQmTpzIXXfdBXRdFvJ1\n",
       "aWlpNDQ0dI9ffPFF4uLiiIuLIz4+vsd0TBEREZEDra6ujsTERGy2ffv1JTU1lfr6+u5xRUVF92eY\n",
       "uLg4Xn755QMdVUQOEofVAUTk0DMMg0WLFnHKKafs1f5lZWWceOKJ3eMf//jHzJ8//2DFExEREekh\n",
       "ISGB2tpaAoHAPhUY5eXlJCQkdI/T0tIoLS09GBFF5CDTzAsR2aPS0lLWrVvHhAkTur+mNS9ERETk\n",
       "UBo3bhwul4vXXnvtW7d/28zRQCDAG2+80eMzjIj0Xpp5ISI9/LeYaGtr45NPPuHWW29lzJgxPe44\n",
       "IiIiInIoxcTEMGfOHG688UYcDgenn346TqeT5cuXk5+fT3h4ePe+Pp+Pbdu2MWvWLHbt2sVtt91m\n",
       "YXIROVA080JEepgxYwbR0dGkpKRw6623cskll5CXl9e93TCMb/2/GyIiIiIH02233cYjjzzCfffd\n",
       "R58+fejbty+PP/549yKeCxcuJCoqitjYWM4//3ySkpJYu3YtKSkp3c+hzzAivZdhav63iIiIiIiI\n",
       "iASx/znzIi8vj5ycHI466ijmzp37je2LFi1i2LBhjBgxgpEjR/Lee+/t9bEiIiIih8o111xDcnIy\n",
       "Q4YM+dbtzz//PMOGDWPo0KGMHz+e9evXH+KEIiIi8l32OPPC7/czaNAgli9fTnp6OqNHj2bBggXk\n",
       "5uZ27+N2u4mIiABgw4YNXHjhhWzfvn2vjhURERE5VD766CMiIyO58sor2bBhwze2r1y5kmOOOYaY\n",
       "mBjy8vKYNWsWq1atsiCpiIiIfN0eZ14UFBSQnZ1NVlYWTqeTSy+9lEWLFvXY57/FBUBrayuJiYl7\n",
       "fayIiIjIoTJhwgTi4uK+c/u4ceOIiYkBYMyYMZSVlR2qaCIiIvI/7PFuI+Xl5WRmZnaPMzIyWL16\n",
       "9Tf2e/3117nrrruorKxk2bJle32sFswRERH5/rR81YH39NNPf+ddlvT5RURE5PvZn88ue5x5sbdv\n",
       "zhdccAGbN2/mjTfeYOrUqfsUxDTNw/7PzJkzLc+gc9V56jx1rjrPw/OPHHjvv/8+zzzzzB7X67L6\n",
       "713/Xg7/c9H5BP8fnU9w/zmczudwOhfT3P/PLnuceZGenk5paWn3uLS0lIyMjO/cf8KECfh8Purr\n",
       "68nIyNinY0VERESstn79eqZNm0ZeXt4eLzERERGRQ2uPMy9GjRrFtm3bKC4uxuPxsHDhQiZPntxj\n",
       "n8LCwu72ZN26dQAkJCTs1bEiIiIiwaKkpISLLrqI5557juzsbKvjiIiIyG72OPPC4XDw2GOPMWnS\n",
       "JPx+P9deey25ubk8+eSTANxwww288sorzJ8/H6fTSWRkJC+88MIejz0STZw40eoIh8yRcq46z8PP\n",
       "kXKuOk85kl122WV88MEH1NbWkpmZyezZs/F6vUDXZ5o5c+bQ0NDA9OnTAXA6nRQUFFgZ+ZA4nP69\n",
       "HE7nAjqfYKfzCW6H0/kcTufyfezxVqkH/Zsbxve65kVERORIp/fSQ0+vuYiIyP7b3/fRPV42IiIi\n",
       "IiIiIiJiNZUXIiIiIiIiIhLUVF6IiIiIiIiISFBTeSEiIiIiIiIiQU3lhYiIiIiIiIgENZUXIiIi\n",
       "IiIiIhLUVF6IiIiIiIiISFBTeSEiIiIiIiIiQU3lhYiIiIiIiIgENZUXIiIiIiIiIhLUVF6IiIiI\n",
       "iIiISFBTeSEiIiIiIiIiQU3lhYiIiIiIiIgENZUXIiIiIiIiIhLUVF6IiIiIiIiISFBTeSEiIiIi\n",
       "IiIiQU3lhYiIiIiIiIgENZUXIiIiIiIiIhLUVF6IiIiIiIiISFBTeSEiIiIiIiIiQU3lhYiIiIiI\n",
       "iIgENZUXIiIiIiIiIhLUVF6IiIiIiIiISFBTeSEiIiIiIiIiQU3lhYiIiIiIiIgENZUXIiIiIiIi\n",
       "IhLUVF6IiIiIiIiISFBTeSEiIiIiIiIiQU3lhYiIiIiIiIgENZUXIiIiIiIiIhLUVF6IiIiIiIiI\n",
       "SFBTeSEiIiIiIiIiQU3lhYiIiIiIiIgENZUXIiIiIiIiIhLUVF6IiIiIiIiISFBTeSEiIiIiIiIi\n",
       "QU3lhYiIiIiIiIgENZUXIiIiIiIiIhLUVF6IiIiIiIiISFBTeSEiIiIiIiIiQU3lhYiIiIiIiIgE\n",
       "NZUXIiIiIiIiIhLUVF6IiIiIiIiISFBTeSEiIiIiIiIiQU3lhYiIiIiIiIgENZUXIiIiIiIiIhLU\n",
       "HFYH2Lp1K6Zpdo9jYmJISUmxMJGIiIiIiIiIBBPD3L05ONTf3DA49thzcDozAPD7PWRmennzzWet\n",
       "iiQiItKrGIaBhW/lvco111zDm2++SZ8+fdiwYcO37nPTTTfx1ltvER4ezrx58xgxYsQ39tFrLiIi\n",
       "sv/2933U8stGnM6hxMY+QWzsE0RG3kd7u9/qSCIiInIYuvrqq8nLy/vO7UuXLmX79u1s27aNv/3t\n",
       "b0yfPv0QphMRsZ7X6+3+pdI0Tbxeb/e2QCCAz+frHvt8PgKBQI9j/+vbjvX7/d3bGhoaaG9vB8Dv\n",
       "91NbW9u9f11dHUVFRXR2dmKaJmVlZZSWlhIIBPB6vezYsYPa2loAWltbKSwspLW1FYDa2lp27NiB\n",
       "x+MhEAhQWlpKWVkZgUAAj8dDUVERdXV1ALS0tFBYWIjb7QZg165dFBcX4/V6u4+tqKjANE06Ojoo\n",
       "Kiqivr4egObmZgoLC2lrawOgurqa4uJifD4ffr+fnTt39ji2sLCQhoYGAJqamigsLKS9vR3TNKmq\n",
       "qupxbHFxMVVVVZimSXt7O4WFhTQ2NgLQ0NBAYWEhHR0dBAIBNm/ezPr16+no6Pgef+u9h+WXjYiI\n",
       "iIgcChMmTKC4uPg7ty9evJirrroKgDFjxtDY2Eh1dTXJycmHKKGIHClM08Q0TWw2G16vl8LCQmw2\n",
       "G9nZ2ZSUlLBp0ybi4uIYOXIkb731Fjt3VpCTM5ABAwbw9NMLaWpq4+yzx+Pz+Vi4cDkul5Nrrjmf\n",
       "NWs2snLlF6SnJ3DVVRfy/POLKS6uZtSoQRx3XC5/+ctLtLd3cv75E7DZbLz++geEhrqYMuUMFi5c\n",
       "xubNO0hIiOGqq85i3ryl1Nc3c+yxAzn++Fyefz4Pvz/AGWeMpbPTy/vvr8HlcnLVVWfz3nvr2Lat\n",
       "hOTkeC6//AyeeWYJTU2tDBt2NEOGDGDhwncIBEzOPHMsJSW72LSpEsPwcNFF43n33U9pajIJD/dz\n",
       "8snDePPNT7HZ4omNdZOensSGDXWAQW5uFHV1rdTWuggEGjn55KNZsWIrPl88dnstJ56Yy3vvfYnd\n",
       "HkdCQjtJSbFs2tQEmAwdGkd5eQMNDWH4/fWcdtoxfPDBJgKBRJzOOsaOHUR+/lbs9hj69PEQHR3B\n",
       "1q1tgI8RIxIpLq6lqSmCQKCOU089hvz8TZhmIi5XPccdl82//12IzRZJerqJyxVCUVEngUAno0en\n",
       "sHVrJa2t0ZhmHaeeOpj33tsIJBIW1sixx/Zl9epSbLZw+vUzABs7d/oJBNoYOzaDL74oo60tBqjl\n",
       "5JOP5b33vsBmSyQsrIH09Hi2bPFjs4WRkdHOvHkPk5iYaOV/1ged5ZeNDB9+F7Gx9wPQ2VlBaOgd\n",
       "vPfev6yKJCIi0qvoEoZ9U1xczHnnnfetl42cd9553HXXXZxwwgkAnHbaacydO5eRI0f22M8wDGbO\n",
       "nNk9njhxIhMnTjyouUXk0GtqamLLli1ERUWRk5PDli1bKCkpITMzk9jYWJ566nlqa1s4+eSRxMRE\n",
       "M3/+EgzDYMqUM1m7dhPvv7+WxMQYrrzyXP75z8Vs315Kbm5/Tj75OB5//GVaW9sYP34ou3Y1UFQE\n",
       "puklPb2DigovpjmWQKAIp3M7nZ3HYRij8HqX0NFRSHT07TidfaitnYNpRpOScg9+fxtlZTcRFXUG\n",
       "iYlTcbvXUVExl9TUO4mMHEVd3d9obFxL//5/xOGIp3Tnz7CTQP/Muwl46tlZeD0pST8nI+UCWho/\n",
       "ZGfRLI4a8DCxUUdRWfYILY2byD36Ppw2F8VFt+I0BtK/3w34ffUUb7+FxPgr6ZM0gdamVVRXPEO/\n",
       "zF8QEZbOrqqnaHdX0j/rJuzYKSu5jxDHMDLSzsXna6S0+AGSEi4nLjaX1uYCancto2/fG3E5Iti1\n",
       "ayGd7Z3063sphgnlZX/EFXIcKX1OwOdtpLL8CRISLiUqMh13y+fU168gPW0qIY5Qamtex+sxSE89\n",
       "B4MAFRVPE+oaRWLCMHzeeqqrXyAh/gLCw/rgbv2cpqYNpKb8EIcthNq6Jfh9YaT0mQiYVFc9S2jo\n",
       "8cTFDsLrraW2Zgnx8ecSGhqPu+UzWloLSe5zLjabk/q6NzEDMSQlnoBp+tm16wXCw8cSHT0Ar6ea\n",
       "urp3SYg/i5CQGFpb1tHmrqRPn0n85ag/sf6LHwMjGDz4HgKBdtauPYGUlIfo2/d0GhtX8OWXt3Ls\n",
       "sS8TFdWXoqKZ1NaWMnr03zEMOzU1/+Css0p56KHfWPyv5tvl5+eTn5/fPZ49e/Z+fXZReSEiItKL\n",
       "qbzYN/+rvPjVr37F+PHjga7y4sEHH+S4447rsZ9ec5HewzRN6uvrCQsLIzw8nKKiIoqLi0lPTycr\n",
       "K4u8vDzq6xsYMWI4nZ2dzJu3CL8/wA9+MIS//vVV2tqy8Pmq6dfPy86dAWy24Xi9a/D763A6r8Hp\n",
       "zKKh4WG83k6Sk3+DaZqUl99GRPgE+va5lkDrBupKfk3/5J+TFDWM1tqXcNe/z6C+dxBhj2JX6Vxc\n",
       "gTQGpJ2J09/OrpJHiI88g6ToVOgsp6l2OcmxpxHutOFzf4HX3USf2KNx4aG9+XMcZhyxETHYAx48\n",
       "7i8Jc6QR5gCb343paSTMEYEDP4a/Hbvpx2mA3fRhQz/DgsmpJ3lZ+9kU4FpGjDgDr7eONWsuIT39\n",
       "n/Ttm0lDw3K2bHmF3NwHiImJZceOh6iqCuX446djtztwuzeTnv4HXnvtSatPZa/s7/uoLhsRERER\n",
       "AdLT0yktLe0el5WVkZ6ebmEiEfk2gUCApqYmoqKicDgclJWVUV9fT1ZWFjt27GDevFfxePyceeZY\n",
       "nntuCZs2VWEYHsaNy2blynJstiF4vRuJjHTT0jICGIin83Zc3gCZkdOIDnQw/7mZ5MZeTmbcsYR0\n",
       "lNGQ9yhnxf+QxNAGjOZGzJZKMqMXEk47ZuuXuPx24uqnEup34/TWEc5abDsf/Sp00c09T2LLNT3H\n",
       "2xZ/9bjxH9C427a6f/bct37LboMqaN5t6N0O3t3Gvvaex+72+6IXOwGbE7/hoNPfjmmLBLsLPwE6\n",
       "vC3YQ/pg2px4fM10+v24wtPwY8fdvpOAEY8rog9+E5pbNxISmoPDFYXH10yreyfhUcMxHCG42wrp\n",
       "8PiJiR9MABv1jSsx7H2Jjs7CZ/qprX+P8MjxhIbF0eGppqnpc2ITTsPuCKWpqYAOT4DEpPEEDDu7\n",
       "ahbjcOYQG5eLL9BB9a7XiY45k7DwJNrattPY9DmJyRdit7uorX8Hj9dJcsqpmEBl5XO4XKOJSzgG\n",
       "r6+JqqoXiUu4mLDwJFpa19PQuIG0tB9js7uo3vUafl8UKamnYxoG5WV/JTT8FOITjsHjqaGycgFJ\n",
       "faYSFpZAc/Mq6hu3kplxOYY9hKqqf+EP9CEt9TRMoLT0USKiziM+fhCdneVUVCwkJeVqQsMSqG94\n",
       "n6bmnfTtOxUTG3a7H8P4HDgDmy0cm60BwygCMrHZwjHNz7Db24BYbDYTm+0jDGMapmmjrW0ZQ4YM\n",
       "+Po/lcOOZl6IiIj0YpoFsG/2NPNi6dKlPPbYYyxdupRVq1Zxyy23sGrVqm/sp9dc5OBraGjA4/EQ\n",
       "Hx/P008/y6JFHxEREcrFF5/EU0+9TnV1O2FhASZMGMI773yJ3Z5GIPAlnZ0OQp03Eh/w4Cn7NX1D\n",
       "TyInYQJRbdvoKHucrJhTSXKAq20LIe5iUlwJRPsbifTW4STwv4PtA4/NRYcRSpO/HX9IOj5nFG2B\n",
       "Nho7mnHFDMVnD6fGvYVWn53opBPx2FyU1bxGIORYohNPxO2rp2zXvwiPO4eQyGNocH9CXesqIuJ+\n",
       "jOlMpNH9Mp0BH67Ii/Hio6ltAXZXLvbQM2n3FdLUtgRX5LkYzuG4PXm0ezfhDP0xAVsCHt8/wAjD\n",
       "4bgc02zEbn+ZQCAOp/ME/P4vSUioo74+CZvtaPz+FURF+WltPRabLQq7/UMCASeBwHhMs5bo6M00\n",
       "N0diGMcTCGwkPr6RhoYUbLaBBAIfERERoK1tGBBKSMjHgBOf71gCgRoyM92UlXkxjBz8/i0MGRLH\n",
       "xo0N2O0phIaWkZwcS1ERGIaNzMxOmpo6aWnpQyBQy4gR8axfXwVkYpolDB+ewdq1u3A4+hARUUlc\n",
       "XCQlJQ5MM8CAAX527WqjvT0Vn6+KUaOS+fTTcgwjAyhl8OA0Pv+8HpstnujoXUREhFFe7gK8ZGdD\n",
       "ZWUrHR1p+P2VHH98KmvWlGMY6dhsZeTkpLBhQxM2WyyxsTW4XCFUV0cSCLQxaJCTkpJGPJ50/P5y\n",
       "jj8+g4KCMuz2dByOUrKzk9m4sRW7PYrExAbARm1tDH5/C4MHh7F9ex0+XwZ+fzmjR2fwySfl2O1p\n",
       "hISUM3hwJgUFpRhGCEOH9uHxx+8nOjr6gP43fLDs7/uoygsREZFeTL9I773LLruMDz74gNraWpKT\n",
       "k5k9e3b36vY33HADADNmzCAvL4+IiAj+8Y9/fOOSEdBrLnKgeb1e3n77baqrd5Gbm8M77/ybl176\n",
       "CMMIITy8haamo4mNvYVARxmtW69jeOJPyYnKIKLubVy1b3N0zBgSA02Et35OvM9DIu79uizCTQht\n",
       "riRaHHHUdFTRakvAFjuUVuzsrH8HI/ZM7DHDqOkoobj+NUKTLsMX2p8a96s0ehsIib2OdpuL2rYn\n",
       "8DnTcYRejt9fRCDwOg7HUOB4DGMFoaGleDxDMIxUDOMDMjNjKCkJYJo+xoxJo63Ny2efbSU6Opxb\n",
       "b72Cd94poKiogmHDsrniivN5+eU8mpraOOecE0lNTWbJkvdwuZxccsl5bNy4iYKCjaSnJ3LRReex\n",
       "ePFSdu6sZsSIQUyYMJ633srD7e7gpJPGY7PZyM//iLAwF+ecczYNDQ1s3bqV5ORkRo4cySeffEJt\n",
       "bS05OTmkpaWxcuVKvF4vI0eOxO/3s27dOsLCwjjhhBMoKipi+/btpKWlMWzYMAoKCqivr+eYY46h\n",
       "T58+rFq1Cr/fz+jRowHYvHkzERERDBkyhPLy8u5LeQYMGEBpaSlNTU1kZWURFhbG9u3bMU2T7Oxs\n",
       "Ojs72bFjB1FRUfTr14/a2loqKipIS0sjMTGRkpISmpub6d+/Py6Xi+3bt2MYBtnZ2XR0dLBjxw5i\n",
       "YmLIzMykpqaGyspK0tPTiY+PZ+fOnbS2tjJw4EAcDgfbt2/HbreTnZ2N2+2muLiY+Ph40tPTqa6u\n",
       "prq6unv9kx07dtDe3s7AgQOx2WwUFhbicDgYOHAgra2t7Ny5k4SEBNLS0qiqqqKmpobMzEyio6PZ\n",
       "sWMHnZ2dDBw4EIDCwkJcLhcDBgygqamJkpIS+vTpQ0pKChUVFdTV1dGvXz+io6OpqanB6/WSkpKC\n",
       "zWb5jUT3msoLERGRI5B+kT709JqL7LvVq1fzxhvvExYWwnnnncb8+a/xySebSE9PIhDwsGFDDC5f\n",
       "NklNT9HXE8lxsafTx1OJs2oBfW2JZBpNxHmq97qUaHImUOn3UmtLxRs3lAZHPJtrF+GLnowz6UQq\n",
       "OorZVDmPmKw5+KOHs7XmSepaC0hJuQvDcOD1Pk6fPiE0NNiBNi6++EQ+/HA9lZUN9OkTw913T+Od\n",
       "d1ZRV9fCKaeMZPDgHF55JQ/DMLjkkrNpbm5m1ap1JCREc8EF57N27VpKSkoZMKA/Y8eO5d///jet\n",
       "ra2MGDGC9PR0ysrKsNvtpKWlYRgGXq8Xh8OBYRgH9y9GxAIqL0RERI5A+kX60NNrLvLt3G439fX1\n",
       "JCcnU1BQwCOPPIvb3UFubjLLl+/AZruKkM5KIqvnMiTsRI4JSSWxIZ8U9xZy7aEkeiv3+Px+bFRi\n",
       "p8Y1iKboHMoNJxvqVmDPvIOOmFy2Na5kU+1CIrPuw7RH0N7+KCEhHhyO4wgEahgyxEFFRRM1NW1E\n",
       "Rzv42c8uZuHC96ira+TEE4fzwx9O4vXX3yUQCPCjH53FiBEjqK2tJSIigoiICEzTpKOjg9DQUJUK\n",
       "It/DQSsv8vLyuOWWW/D7/Vx33XX88pe/7LH9+eef58EHH8Q0TaKiovjrX//K0KFDAcjKyiI6Ohq7\n",
       "3Y7T6aSgoOAboVVeiIiI7D/9In3o6TUX6bqLx7Jl77BmzUZSUxOIj49jzpy/4/dHY7NV094awrGu\n",
       "a8jprCC25EGOs6UzxKygT2fZdz6nxwih1JnIl14brakXUhvWn00t/6aocxsdSdOosfuxhbyGacZg\n",
       "tw/D79/KyJHxfPppGYYRT2xsO3fccSUffvgpnZ0+fvSjMxg8eDCbNm0iPDycIUOGYBgGLS0tREZG\n",
       "9qpp9iKHk4NytxG/38+MGTNYvnw56enpjB49msmTJ5Obm9u9z4ABA/jwww+JiYkhLy+P66+/vntx\n",
       "K8MwyM/PJz4+fp+DiYiIiIiItXbt2kVbWxvp6el8/vnnvP76cpxOO+DjxReLsNnOwenOJ3XXUi5P\n",
       "nEKup5SM2i842ltLGG/t9kzlQFdBUYidstCxNCSMYGdICvllT9CWdhe+1HOpa3wRr3cBYWEt2GyF\n",
       "pGSH8otf/IGNG7cQERHJ+ee/Qnt7O4WFhaSmXsGgQYNobGyksbGR1NRUXC4X5557bo9zGDduXI9x\n",
       "b1nUUER62mN5UVBQQHZ2NllZWQBceumlLFq0qEd5sfsPgzFjxlBW1rNN/V+Nyj+2zWd1ciwv9P3F\n",
       "vmYXEREREZEDLBAIYBgG99//KC+88CE2WxSRkbU0NLiw266hT2cxmTsfZXbMaRzX/msGuDd2Heie\n",
       "1eN5qlx9KYwcxqe+Vgo662kdcC/Fjmhq6u8lNDQZp3MEhrGR3PMmEMYnVFa+xemnH8PMmW9SWVmJ\n",
       "x+MhJyeHsLAwTjnllB7PnZmZ2f04NjaW2NjYg/2yiIjF9lhelJeX9/jBkJGRwerVq79z/6effpqz\n",
       "zz67e2wYBqeddhp2u50bbriBadOmfeOY193l7KyaR3GgjfDwwYSG7s9piIiIHBny8/PJz8+3OoaI\n",
       "HIY2btzI7bc/QFlZFXFxLnbtSiEt+TmyO7YT9+mVjPNHMsH4GUmdXbMoqH0WgE4jhPWEUBJzFuWJ\n",
       "E/jccPBO5aNEZNyIYSTgcLzKpZdOYtOmFYwMC2H69Cdwu91s3LiZ1NSxnHPOOTidzh5ZNHNbRL5u\n",
       "j+XFvixE8/777/PMM8+wYsWK7q+tWLGC1NRUampqOP3008nJyWHChAk9jpsF7MCgOGsWnZ0VwKv7\n",
       "kl9EROSIMnHiRCZOnNg9nj17tnVhRKRX6+zs5M9//jsffPAZcXFhbNhQiGHcy/CIeI7acB3jW7dz\n",
       "QlEaEf6WHsc1O+JYYYRTEJJFad8ZfGpz0Nz5MCEhnYSEFGGz7eDxRx5l164a2tpamThxDoMHD/7G\n",
       "9//67wUiInuyx/IiPT2d0tLS7nFpaSkZGRnf2G/9+vVMmzaNvLw84uLiur+empoKQFJSEhdeeCEF\n",
       "BQXf+kMqo30bNtO33ychIiIiIiL/W2VlJR9++CE2m40VKz5j2TI7sZG3EfXZE1xVtZULnVfTr31r\n",
       "j2MqQvuz0h7BRwEfZVm/odCZhC/wZ045JYddO95ldFoCv/rVAux2OzU1NfTt25fExESLzlBEDld7\n",
       "LC9GjRrFtm3bKC4uJi0tjYULF7JgwYIe+5SUlHDRRRfx3HPPkZ2d3f31trY2/H4/UVFRuN1uli1b\n",
       "xsyZM7/1+zhNL+nthWy3Rx2AUxIREREREYCWlhaWLHmTpqYWMjPT+O1vn6Kl5SQifE3kFP+DR6JO\n",
       "ZNy2CcT46rsO8EGLI5aVsSfzaucatqQMoTEik8TEJqZOPYeGd9cwKsTB9dffy+jRo7/x/Xa/5FxE\n",
       "5EDaY3nhcDh47LHHmDRpEn6/n2uvvZbc3FyefPJJAG644QbmzJlDQ0MD06dPB+i+JWpVVRUXXXQR\n",
       "AD6fjym1rwvyAAAgAElEQVRTpnDGGWd85/fKbPuS7VHf/AEoIiIiIiJ7r6KigvLycuLi4rjlljkU\n",
       "FR0DpNFZdTdTjOFcEHiDoU0f4jB9UPcSAKVhR7HE8PBBdD+2Jp6Lz1jHHXfM5Vc/GIfb7WbgwIGE\n",
       "hoZy5ZVXWHtyInLEMkwLb1RuGAb//eZ/G/AA85KvJDT0Dt57719WRRIREelV9vde6bL/9JpLsGlp\n",
       "aaGoqIjo6GjWrVvPnDnzsNkG0NDwEab/JC5OmMRZlc9w4q4XCcUPgN+w80lIGkttEaxLv5EiZzvZ\n",
       "2V9w553XUl9fz8CBA791nQoRke9rf99H9zjz4lDq595sdQQRERERkaBXU1PDhx9+iGEYpKWlcccd\n",
       "D+F2p9PZuZOGhhoGDHiFjICXcS2buaD+72SV/R6AAAbLbUmsGPBrVsSeRJn7UaZOHcS4gIcLU5L4\n",
       "0Y/+TFSULuMWkeAUNOVF3zaVFyIiIiIi3yYQCODxeKipqeGyy26hoWEsAJWVM0lN/T19+kyivfFj\n",
       "RtTNYIb7Csa0vI/tP3OcK5zJLE2+nAUuD+G5ddTX52OzfchdN13EFVdcuk93GBQRsUoQlRdfgqZg\n",
       "ioiIiIj0sHjxEmbPfpyODj82Wyc+3zWkpFwJQGHhy0Q3uvhZ862cXjWfWF89eMFjhJAfezIvRlVQ\n",
       "O3Qkze4qzjhjDLfd9gghISEWn5GIyL6zvLxotocS7e8gwt9CkqeSljCrE4mIiIiIWGvnzp2UlJTg\n",
       "dru59975REb+naioVD7//IfY7U5SUiC5o5i/mjVMqTiNkP+sZbE5JJLX49N4K/5YPFEBHnvsGUaN\n",
       "GmXx2YiIfH+Wlxc7XAkMaysHIKt9OxtiLA4kIiIiImKhV15ZxJw587HZcqivX04gMJmEhHQAUlIu\n",
       "JVD0OLdsWsI5NS/iMH34gaWxWfwzMYNT77iGW6+6jCvr6khMTMTlcll7MiIiB4jl5UVR6O7lxTY2\n",
       "WJxHRERERMQqDQ0NzJnzFJGRfyckJAWvdxTbt/+DzMx2+gcquLnmX5zj+QjnLhM/sHXMOLKe+huD\n",
       "o6N5IiqKuLg4ANLT0609ERGRA8zy8mJHaGL3437t2yxMIiIiIiJy6LndbmbPfpjly1fjcJi43ZHE\n",
       "x6cAkJg4mfCKOdyxcQiTW3bgIIBpt8OUKdjvuYejjz4agL5WnoCIyCFgfXnhSuh+3K+9EOhnXRgR\n",
       "ERERkUPst799lCVLQkhIWEBb23YqKqYSGvoRQyPTmbL9Zs5s+Aw7ELDZaLvkx4Tfdx9kZ1sdW0Tk\n",
       "kLK+vAj9qrzIat+GygsREREROdxVV1fzzjvL8fv9vP32x8THP4fDEU109HGkJ5/PVdVXMmNTKWGm\n",
       "n4DdDj/5Cba77yZ8wACro4uIWMLy8qIyJAaPzUVIoJMEbw2RXo/VkUREREREDprS0lIuu+wW6utP\n",
       "ApyUl5fQt+9WEhPHclTzGh6veobcjmoAApddhu3++yEry9LMIiJWs7y8CBg2SsIGke1eD0C/tiaL\n",
       "E4mIiIiIHDzz5i2koeFCkpOvAKCzs5nmypu4vTKKqXXvY8ck0K8ftiefxDZpksVpRUSCg+XlBUBJ\n",
       "RG53edHX3WxxGhERERGRA2vdunXMnPkYtbUNeL0d2Gw3d287y3Dxm/bN9GlrxbTZ8P38Jhy/+x1E\n",
       "RFiYWEQkuARFebEzPLf7cd82lRciIiIicvgoLS1l2rQ5wF2EhQ2kvPweWlv/QJozjttKHmBS3aKu\n",
       "HUeMwPj733GMHGlpXhGRYBQU5UXJbuVFP5UXIiIiItLL+Xw+XnrpVTZsKKS1tRqPZyyJiWMAyOr3\n",
       "J0Z+cTSzNvyAGJ8HX0gI9t/+FuO228ARFB/PRUSCTlD8dOwx88KtNS9EREREpPcyTZN7732AN95o\n",
       "xm4/hebmF2lqqiI+PkCsv567Nl7M2KaSrp1POw3HE0/AwIHWhhYRCXJBUV6UhR+NHxt2AqR0uKG9\n",
       "HcLCrI4lIiIiIrLPamtrefPNtSQmvojNFkJs7Cls2DCOiKKf8Jfqt8jw1uKJiiLkscdg6lQwDKsj\n",
       "i4gEvaAoL7w2F5VhA8ho344NYOtWGDbM6lgiIiIiInvF6/Xypz/9jTffXIHTadDW5iUhoeujtt3u\n",
       "4qqoeB6sXkiI10PbMccQvmwZpKdbnFpEpPewWR3gv3a/dITNm60LIiIiIiKyj/74xyd5+ukS2tvn\n",
       "Ult7M/X1pZSV/R9treu5+Ivz+UPpu4R4PDBlCuFr1qi4EBHZR0FTXpSE53w1UHkhIiIiIr3IkiUr\n",
       "iI29idDQTKKjjyc5eTqjcz/jD5UXcmPNYkzDgAcfhGef1eXRIiL7ISguG4GedxxReSEiIiIiwe6z\n",
       "zz7j6adfxuPx09Hhxu+vweXqmlGR4dvJ4+tXE1deAtHRGAsWwNlnW5xYRKT3CpryYmeEygsRERER\n",
       "6R02btzIT34yG9O8AZstnIaGAmy2X+J2T2GUeyV/qvwHsd5OOPpoWLQIcnL+95OKiMh3CpryosfM\n",
       "i61bwefTfa5FREREJCi99trb+HxTSEo6EwCb7X5SU//ML6OXMf7FF7D5/XDmmbBgAcTGWpxWRKT3\n",
       "C5o1L9yOGGqcyV0Djwd27LA2kIiIiIjId7DZDEwz0D22Bzq5det6Jix4vqu4uOMOWLJExYWIyAES\n",
       "NOUFwM6w7K8GunRERERERILUxRefg8v1L2pqXqOpbim/LZrCqds2gMsF8+fDQw+B3W51TBGRw0ZQ\n",
       "XZdRHH4Uo5pXdA02b4bJk60NJCIiIiLyH3V1dTz55HzKy+sYN24wzz77O55/9lUueONVjm8ug+ho\n",
       "ePttGDvW6qgiIoedoCovVjau4uL/PH71gT9wz7w8kpOjyM9fbGkuERERETmyud1upky5ibKyk3A6\n",
       "R5Kf/xpXTKng/pYq2PQZhIfD0qUqLkREDpKgKi++8H8VJ8fsR0rK+1RVnWxhIhERERER+OSTT6io\n",
       "6EtS0vUA+H3HkfzoYKjd2XWpyOLFMH68xSlFRA5fQbXmxVZbWPfjvu7NYJoWphERERER6RIIBACj\n",
       "e3xl6YNcU7sT0+GAl16CU0+1LpyIyBEgqGZeVBJCE5HE0Eqkv5kETyVVVocSERERkSNSbW0tv/71\n",
       "7/nssy2kpiYQFVVDTc08rmn8lOvK/0TAMLA99xycd57VUUVEDntBNfMCw2CrfUD3sG+b7jgiIiIi\n",
       "IodeIBBg+vS7+eijo7Hbn6Ko6Ed4vT5mp7/KbeV/AsD829/gxz+2OKmIyJEhuMoL6FFe9FN5ISIi\n",
       "IiIWqK+v58sva0hMvBqnM4G4uDM4vRouemdJ1w5//jP2666zNqSIyBEk+MoL227lhVvlhYiIiIgc\n",
       "emFhYRhGJz5fIwAn7nqJ2SVvYZgm/N//wYwZFicUETmyBNWaFwBbvn7ZSLSFYURERETkiNLQ0MDn\n",
       "n39OWFgY06f/kL/85RbGNcXzm7I/4cDEvOcejF/+0uqYIiJHnKArL3rMvGjbDORYF0ZEREREjhiF\n",
       "hYVcddUvaGnJxTTrGTHCwbPTjmPInXfiIEDg5pux/fa3VscUETkiBV15sdOWjsfmIiTQSYKniih/\n",
       "ttWRREREROQIcN99f6G5+RoSEs7BNAOUfHwbx7z2axxeL1x/PbZHHwXD+N9PJCIiB1zQrXkRMOyU\n",
       "hh3dPR7gabMwjYiIiIgcKUpLdxERMRgAOwEeqngbV0sLnHkmPP64igsREQsFXXkBUBL+1aUiAzrd\n",
       "FiYRERERkcNZW1sb77zzDm+++SZDhmTR3PwypulnauFdjGr7ks7ERJg/H+x2q6OKiBzRgu6yEYCS\n",
       "8Nzux5p5ISIiIiIHQ0tLC1dccRNFRSkYRjShoesZPDiZqNVjubJsDQHDIOSllyApyeqoIiJHvKCc\n",
       "ebEz4qvyYqDKCxERETlA8vLyyMnJ4aijjmLu3Lnf2F5bW8uZZ57J8OHDGTx4MPPmzTv0IeWQefHF\n",
       "V9i27RgSEx8gIeEuOjt/SobDyd/aS7ABtlmzMCZOtDqmiIgQpOVFj5kXnSovRERE5Pvz+/3MmDGD\n",
       "vLw8Nm3axIIFC9i8eXOPfR577DFGjBjBZ599Rn5+Prfffjs+n8+ixHKwVVc3YLN9tTh8uKs/U5ct\n",
       "wrZrF5x8Mtxzj4XpRERkd0FZXpSGHU2ArgWRMrzt0NFhcSIRERHp7QoKCsjOziYrKwun08mll17K\n",
       "okWLeuyTmppKc3MzAM3NzSQkJOBwBOVVtnIAjBs3HNNchMdTjd/fzo+Lf8bw2oquy0Sef17rXIiI\n",
       "BJGgfDf22MOoDO1PekcRdoCtW2HoUKtjiYiISC9WXl5OZmZm9zgjI4PVq1f32GfatGmccsoppKWl\n",
       "0dLSwosvvvitzzVr1qzuxxMnTmSiLi3oNbxeL0uXLqWioprBg3O5887T+fOfr2ZwQw031a7t2um5\n",
       "5yA11dqgIiKHifz8fPLz87/38wRleQFQEpFLekdR12DzZpUXIiIi8r0Ye3Gby/vvv5/hw4eTn59P\n",
       "YWEhp59+Op9//jlRUVE99tu9vJDew+/387Of/YoVKxyY5mDs9qe45ZZTWJP3TxgxAsM04a674Iwz\n",
       "rI4qInLY+HrJP3v27P16nqC8bARg527rXvDll9YFERERkcNCeno6paWl3ePS0lIyMjJ67PPxxx9z\n",
       "ySWXADBw4ED69+/Pli1bDmlOOXg+/fRTVq9upU+fB0hJmUps7B/40x+ex7zqKozychg/HubMsTqm\n",
       "iIh8i6AtL0rCc74afG0xLREREZF9NWrUKLZt20ZxcTEej4eFCxcyefLkHvvk5OSwfPlyAKqrq9my\n",
       "ZQsDBgywIq4cBG1tbdjtiRhG10dghyOGqbWl2N56C+LjYcEC0BonIiJBKWh/Ou9+xxGVFyIiIvJ9\n",
       "ORwOHnvsMSZNmoTf7+faa68lNzeXJ598EoAbbriBu+++m6uvvpphw4YRCAR48MEHiY+Ptzi5HCiD\n",
       "Bw8mPPyPNDQsIzx8CH0rH+bWXVu7Ns6bB7utiSIiIsHFME3TtOybGwbDh99FbOz9AKxaNYHQ0CcY\n",
       "PvxYIr0NvLHiPx8WXC5wu7Xis4iIyNcYhoGFb+VHJL3mvdvWrVuZNetPNBWX8+wX7xPf3AS33QYP\n",
       "P2x1NBGRI8L+vo8G7cyLVmcc9SHJxHuqobMTioth4ECrY4mIiIhIL+Lz+Zg/fwGrV2+iX78+TJ/+\n",
       "E/71/J/h4othZROMHg0PPGB1TBER+R+CtryArkU74z3VXYPNm1VeiIiIiMg+mT37IV55pYHQ0PNZ\n",
       "sWI9K1bczKuXT8L16qsQEwMLF0JIiNUxRUTkfwjaBTvha3cc0boXIiIiIrIPOjo6ePXVfJKS5hAT\n",
       "M56kpOnUlMRi3n571w7/93/Qv7+1IUVEZK8EdXmhRTtFRERE5PswDKPH+KqatYRWV8PQoTBtmkWp\n",
       "RERkXwV1ebEzQuWFiIiIiOyf0NBQLrjgB9TWzqKp6WPsFQ9wbc3qro1//KMWgxcR6UWCes2LHjMv\n",
       "vvwSTBO+1p6LiIiIiHyXmTPvpH//BRQUvMHPVy0jNODvWqxz4kSro4mIyD4I6pkXtSFpNPOfsqKx\n",
       "kQlHn8jEiZOtDSUiIiIiQa25uZkVK1bwySefAHDttVfy5JXnMnj9OnC54KGHLE4oIiL7KqhnXmAY\n",
       "bDFCGG12AjAq4j7yqudYHEpEREREglVZWRlTp95GQ0MWgUALQ4faeOpvDxF6881dO9x5J2RlWZpR\n",
       "RET2XVDPvAD40nB2P+7XpnUvREREROS7PfDA49TWXkJc3IPExz/OunXJrLnpFli7FtLT4Ve/sjqi\n",
       "iIjsh15QXnx13+2+Ki9EREREZA9KSnYRHj4M6LrTSDRHMXzhC10b586FiAgL04mIyP76n+VFXl4e\n",
       "OTk5HHXUUcydO/cb259//nmGDRvG0KFDGT9+POvXr9/rY/eGZl6IiIiIyN4aPTqH1tbXME0/Pl8L\n",
       "1+16kMjWFhg3Di6/3Op4IiKyn/a45oXf72fGjBksX76c9PR0Ro8ezeTJk8nN/eouIAMGDODDDz8k\n",
       "JiaGvLw8rr/+elatWrVXx+6N3cuLvu7N7NzpIDf35O6vJSdHkZ+/eJ+eU0REREQOT7ffPp3Kytl8\n",
       "9NFk+nY2c3Xjhq4Nf/yj7lonItKL7bG8KCgoIDs7m6z/LGp06aWXsmjRoh4FxLhx47ofjxkzhrKy\n",
       "sr0+dm/swInHCCHE9JDkqSDCmUVKyvvd26uqTt7D0SIiIiJyJImIiOCvf32Q5uZmIqZMwb7dDz/5\n",
       "CYwebXU0ERH5HvZYXpSXl5OZmdk9zsjIYPXq1d+5/9NPP83ZZ5+9T8dWVX1EY+MsAAKBpm9s9xsG\n",
       "5eFH0d/9BQCDTM+eIouIiBzW8vPzyc/PtzqGSFBZvHgJDz88n7a2ds499wfcddfNRK9aBUuWQGQk\n",
       "3H+/1RFFROR72mN5YezD1Lr333+fZ555hhUrVuzTsSkpE4iNnQVAVdW737rPzvDc3coLL0V7nUpE\n",
       "ROTwMnHiRCZOnNg9nj17tnVhRILAmjVruOee54iIeACXK56FCx8m3PkX7nz+qa4d7r0XUlOtDSki\n",
       "It/bHsuL9PR0SktLu8elpaVkZGR8Y7/169czbdo08vLyiIuL26dj90ZJeE734xzTo/JCRERERAD4\n",
       "+ONP8PvPJyxsIAAxMdcRNv8S2LIJBg6EW26xOKGIiBwIe7zbyKhRo9i2bRvFxcV4PB4WLlzI5MmT\n",
       "e+xTUlLCRRddxHPPPUd2dvY+Hbu3SsK/Wicjx/Tu13OIiIiIyOEnPj4a0yzpHoe2buAnRf9ZpPPh\n",
       "h8HlsiiZiIgcSHuceeFwOHjssceYNGkSfr+fa6+9ltzcXJ588kkAbrjhBubMmUNDQwPTp08HwOl0\n",
       "UlBQ8J3H7o+dKi9ERERE5Fucf/5kFi6cwY4dM4FEflP9KJHeTjjtNNjP/3EmIiLBxzBN07TsmxsG\n",
       "w4ffRWxs1yJKq1ZNIDT0CYYPP7Z7n48/HsjJYzaw9KNIbJj4gbN+0IHX1tWiV1WdzObN73/b04uI\n",
       "iBz2DMPAwrfyI5Je8+Djdrt59913cW3dyhm//GXX2muffQaDB1sdTUREvmZ/30f3eNlIsOi0h1Md\n",
       "2g8AO5Devs3aQCIiIiISNCIiIpg8eTKTCgowAgH46U9VXIiIHGZ6RXkBPS8dyXJvsjCJiIiIiFip\n",
       "urqaO++cw8UX/4z77/8DbrcbduyAV14BpxPuvtvqiCIicoDtcc2LYFIUOZSx9W8BcHTLWvL7/Mji\n",
       "RCIiIiJyqLW1tXHVVbdRXj6JsLCL2Lz5TYqLZ/JkmLdr1sUVV0BamtUxRUTkAOs15cWXUaO7Hw9q\n",
       "WWNhEhERERGxyqZNm6iqSiQx8UoAwsOP4Yt/nwMlH3XtcPvtFqYTEZGDpddcNrI1alT346Nb1mCY\n",
       "AQvTiIiIiIgV7HY7gUB792Jvpunh4rodGG43nH46DB1qcUIRETkYek15Ue3qS4MzCYBIfzPp7dst\n",
       "TiQiIiIih9rgwYMZOjSEmpr7qat7i8aaX3Bte2XXRs26EBE5bPWa8gLDYMtusy8GtXxiYRgRERER\n",
       "sYLT6eTvf3+IW29NZ/Lkz/n7qRDd0tx1d5EzzrA6noiIHCS9Zs0LgC1Ro7sX7RzUsoZ3k6dYnEhE\n",
       "REREDrWwsDCuu+4nYJowfHjXF2+/HQzD0lwiInLw9J6ZF9Bj5kWOZl6IiIiIHNmWL4f16yElBS67\n",
       "zOo0IiJyEPWymRdflRfZLZ9iM30WphERERGRQ2X16tWsX7+RpKQEzj77bEJCQuDhh7s2/vzn4HJZ\n",
       "G1BERA6qXlVe1LtSKcNOBn7CAm30c2+mwupQIiIiInJQLVjwEr/73ev4/WdgGKt57bX3eOrWa3C+\n",
       "/TaEh8NPf2p1RBEROch6VXkBsNZwkWG2AV3rXqzUpY0iIiIih61AIMDcuU8TE/NPQkKSMc0An356\n",
       "M/X33EMywDXXQHy81TFFROQg61VrXgCstX01JVB3HBERERE5vPl8PrzeAE5nIgCGYSPJF0bSsmVd\n",
       "C3TecovFCUVE5FDofeWFsXt5scbCJCIiIiJysIWEhDBhwnBqav6Ix1NNY2M+VzQuwubzwYUXwsCB\n",
       "VkcUEZFDoNeVF+t2Ky8Gtn6O0wxYmEZEREREDraHHvo155zTit3+c47Nepap7qquDbffbm0wERE5\n",
       "ZHpdeVFv2CkPHQBAiOnhqE63xYlERERE5GCKioriwQd/w4cfvshzp47A0dwMY8fCCSdYHU1ERA6R\n",
       "XrdgJ8DWqFGkdxQBMKS9xeI0IiIiInKgvf32OyxcuIyQEAfXXfdDRo0aBX4/PPpo1w533GFtQBER\n",
       "OaR6ZXnxZfRoTq55EYDBHSovRERERA4neXnLuOOOfxISciOBQDurVt3PP/85k2GFhVBUBAMGwAUX\n",
       "WB1TREQOoV5ZXmyJGtX9eHBHs4VJRERERORAe/75t3C5biI6egwANTVNvP76MoYte71rh1tuAbvd\n",
       "woQiInKo9bo1LwC2RR5HAAOA7M42aGuzOJGIiIiIHCh2uw3T9HaPTdNDv4pS+PhjiI2Fq6+2MJ2I\n",
       "iFihV5YXbY5oSsMHAeDAhM8+sziRiIiIiBwo1113IT7fH6mre5OampcJDX2BH+7c2rVx+nSIjLQ2\n",
       "oIiIHHK98rIRgC+jRtOv7cuuwZo1Wm1aRERE5DBx4okn8tRTIbzyyju4XA5+8oMZRE2aBE4nzJhh\n",
       "dTwREbFAry0vtkaNYlL1s12DTz6xNoyIiIiIHFDHH388xx9/fNfgppsgEICpUyEtzdpgIiJiiV55\n",
       "2Qh0zbzotmaNdUFERERE/p+9ew+Lss7/P/4aGDwgoCKHIUBRQRnzWKhZaViaYS5taR52K2s7sJVZ\n",
       "u9u2bfUtbdtNt7ay3ANbu50zrd+uUpvkCdI0JQ9ppSapIKDgAVEQEZiZ3x8jM+IBT8A9zDwf13Vf\n",
       "3J/7vmd43Y3k7ZvPAU3n6FHprbec+7/+taFRAADGabHFi+1B/WQzHZ9l+ocfpMOsOgIAANBSLVz4\n",
       "ua65Zrwuv/xGPfHEH1VVVeU88b//SeXlUlKS1LevsSEBAIZpscWLY/6B2tmut7PhcEjr1xsbCAAA\n",
       "ABdk48aN+t3v/qWqqucUGDhH8+fbNGPGa86TH3zg/PqznxkXEABguBZbvJCkH4KT3A3mvQAAAGiR\n",
       "vv56nWprRyswsIfM5hB17Hifli37Wiorc/a8MJmkCROMjgkAMFCLLl4w7wUAAEDL1759sKR8V7uq\n",
       "Kl8dO4ZI//2vVF0tDR/ORJ0A4ONadPFiGz0vAADAecjMzFRiYqISEhI0c+bM016TnZ2tAQMGqHfv\n",
       "3kpOTm7egD7qxhtvVGLiLu3b96T27XtNdvvzeuqpNPeQkUmTjA0IADBci10qVZJ2tOujapNJrRwO\n",
       "aedO6cABqVMno2MBAAAPZLPZNGXKFC1ZskTR0dEaOHCgUlNTZbVaXdeUlZXpwQcf1Oeff66YmBjt\n",
       "37/fwMS+IzAwUO+/P1tLly7V0aNHlZT0srq2aSMtWyYFBEhjxxodEQBgsBbd86LWr5W2tg5yH2Do\n",
       "CAAAOIOcnBzFx8crLi5OAQEBmjhxohYsWFDvmg8++EBjx45VTEyMJCksLMyIqD6pbdu2GjNmjG69\n",
       "9VZ17dpVmjdPstul0aOljh2NjgcAMFiLLl5I0ndtgt0NihcAAOAMioqKFBsb62rHxMSoqKio3jW5\n",
       "ubkqLS3V8OHDlZSUpHfffbe5Y6LOnDnOr6wyAgBQCx82Ip1UvGDeCwAAcAYmk+ms19TU1Gj9+vVa\n",
       "unSpKisrNWTIEF1xxRVKSEiod920adNc+8nJycyN0di2b5fWrJGCgqQxY4xOAwC4CNnZ2crOzr7o\n",
       "92nxxYtv24a4G/S8AAAAZxAdHa2CggJXu6CgwDU8pE5sbKzCwsLUtm1btW3bVsOGDdPGjRsbLF6g\n",
       "CdT1uvjpT6XAQGOzAAAuyslF/unTp1/Q+7T4YSM7WwW6/1IrKpL27DE2EAAA8EhJSUnKzc1VXl6e\n",
       "qqurNXfuXKWmpta75qabbtKXX34pm82myspKrVmzRr169TIosXcrKCjQL37xGyUnT9SUKU+4J0d1\n",
       "OKT333fuM2QEAHBciy9e2Ewm6bLL3AfofQEAAE7DbDZr9uzZGjVqlHr16qUJEybIarUqPT1d6enp\n",
       "kqTExETdcMMN6tu3rwYPHqx7772X4kUTqKys1J13/lZr116l6uqXlJ2doPvue1w2m03auFHaulUK\n",
       "C5NGjDA6KgDAQ7T4YSOSpKQk6csvnftffy395CfG5gEAAB4pJSVFKSkp9Y6lpaXVaz/66KN69NFH\n",
       "mzOWz3FOjBqmTp1ukSSFhd2p7dsXqbi4WNF1Q0bGj3cukwoAgLyg54UkaeBA9z49LwAAADxa27Zt\n",
       "ZbMdlN1eI0my2ytlt1eobevW7vkuJk0yMCEAwNN4T8+LOl9/7RwreQ4zigMAAKD5JSQkaOTIeGVm\n",
       "PiaHI0l+fit0xx0jFbpli1RQIHXuLF15pdExAQAexDuKF/HxUvv20qFD0v790q5dUpcuRqcCAADA\n",
       "aZhMJv35z09r+PCF2rVrt3r2vFXXXnut9MADzgsmTZL8vKODMACgcXhH8cLPT7r8cmnZMmf7668p\n",
       "XgAAAHgwf39/jRkzxn2gpkb66CPnPquMAABO4j0lbea9AAAAaLkWL5YOHJAuvVTq08foNAAAD+M9\n",
       "xYuT570AAABAy/HBB86vkyYxdxkA4BTeU7w4sefFunWS3W5cFgAAAJy7I0ek+fOd+6wyAgA4De8p\n",
       "XnTuLIWFOfcPHZJ+/NHYPAAAADg3n3ziLGBccYXUrZvRaQAAHsh7ihcmE/NeAAAAeDCHw6Hy8nLV\n",
       "1tbWPzFnjvMrE3UCAM7Ae4oXEvNeAAAAeKji4mKNG3efhgyZqEGDUvXJJ/9znigtlRYudK4eN368\n",
       "sSEBAB7LO5ZKrUPPCwAAAI/061//Qdu2XauwsImqri7Sk08+oh494tVz+XLnMqkjR0qRkUbHBAB4\n",
       "qNoptUAAACAASURBVBZfvMjP3yGrdbgkKaz2mFbUnVi/Xqqtlcwt/hYBAABaNLvdro0btyo8/FWZ\n",
       "TCa1bh2jioortXXrVvWsW2WEISMAgAa0+GEjNptZFkuWLJYsmWNWqdjc2nmislLautXYcAAAAJCf\n",
       "n58iIjrpyJHvJEl2e40cjq2KlqQvvpBat5ZuvtnQjAAAz9biixcn+7ZNsLvBvBcAAAAeYebMR2W3\n",
       "P6ODB59Raem9uvHGWF3244+SwyGNGSO1b290RACAB/O6MRXftwnWyIr9zsbatdJddxkbCAAAABo0\n",
       "aJA+/fTv2rp1qzp06KD+/fvLVDdf2aRJxoYDAHg8rytefNuWnhcAAACeKCoqSlFRUc5Gbq60bp0U\n",
       "EiKNHm1sMACAx/O6YSPfnzhsZONGqbrauDAAAAA4vc8+c34dM0Zq29bYLAAAj+d1xYtD/gFSt27O\n",
       "RnW19O23xgYCAADAqRYtcn694QZjcwAAWgSvK15IkpKS3Ptr1xqXAwAAAKc6dkzKznbujxhhaBQA\n",
       "QMvgncWLusmfJOa9AAAA8DSrVjmXte/TR6qbAwMAgAactXiRmZmpxMREJSQkaObMmaec37p1q4YM\n",
       "GaI2bdroL3/5S71zcXFx6tu3rwYMGKBBgwY1XuqzObHnBcULAAAAz1I3ZOT6643NAQBoMRpcbcRm\n",
       "s2nKlClasmSJoqOjNXDgQKWmpspqtbqu6dSpk1577TXNnz//lNebTCZlZ2crNDS08ZM35LLLJJPJ\n",
       "uW74999L5eVScPDZXwcAAIBGs2PHDi1atFR+fn4aPXqUYmJinCcoXgAAzlODPS9ycnIUHx+vuLg4\n",
       "BQQEaOLEiVqwYEG9a8LDw5WUlKSAgIDTvofD4Wi8tOcqJETq18+5b7NJy5c3fwYAAAAftmXLFo0f\n",
       "/2vNmuWnl1+2ady4h5SXlyft2yetXy+1bi0NHWp0TABAC9Fgz4uioiLFxsa62jExMVqzZs05v7nJ\n",
       "ZNKIESPk7++vtLQ03XvvvadcU1y8QmVl0yRJdvuhc37vs7ruOumbb5z7S5ZIN97YeO8NAIBBsrOz\n",
       "lV030SHgwf7xjzmqrr5HFssYSdK+fSF66615mtbz+LPlsGEskQoAOGcNFi9MJtNFvfnKlSsVFRWl\n",
       "ffv2aeTIkUpMTNTQkyrsFstQdegwTZJUXLz0or5fPdddJ9XNwbG0Ed8XAAADJScnKzk52dWePn26\n",
       "cWGABpSXH5XZ3MnV9vfvpPLybQwZAQBckAaHjURHR6ugoMDVLigocI9VPAdRx2ePDg8P180336yc\n",
       "nJwLjHkBhg6V6oayfPutVFLSfN8bAADAx6WmDtOxY6+rsnKrjhz5Tjbb2xpz41CKFwCAC9Jg8SIp\n",
       "KUm5ubnKy8tTdXW15s6dq9TU1NNee/LcFpWVlSovL5ckHTlyRIsWLVKfPn0aKfY5CAqSrrjC3V62\n",
       "rPm+NwAAgI+76aYxeuqpFIWGzlBExEv6058marglUtq9W4qMdC6TCgDAOWpw2IjZbNbs2bM1atQo\n",
       "2Ww23X333bJarUpPT5ckpaWlqbi4WAMHDtThw4fl5+enWbNmafPmzdq7d69uueUWSVJtba1+/vOf\n",
       "6/rmrrCPGCGtWOHcX7pUmjSpeb8/AACAjzKZTJo06VZNmnSr++Arrzi/Xn+9c2U4AADOUYPFC0lK\n",
       "SUlRSkpKvWNpaWmufYvFUm9oSZ2goCB9UzdhplGuu0565hnn/pIlzqVT+YsSAADAGHVDRkaONDYH\n",
       "AKDFaXDYSIs3aJBz+Igk5edLO3YYmwcAAMBXHTsm1a2UM2KEoVEAAC2PdxcvAgKka65xt5csMS4L\n",
       "AACAL1u5Ujp6VOrbVzo+qTsAAOfKu4sXknPoSB2WTAUAADAGq4wAAC6C9xcvTuyWuGyZZLcblwUA\n",
       "AMBXUbwAAFwE7y9e9O4tRUQ49w8ckDZuNDYPAACAr9m7V9qwQWrTRrr6aqPTAABaIO8vXphM0rXX\n",
       "utsMHQEAAGgSDodDO3bs0MaNG3XkyBH3ibp5x4YNk9q2NSYcAKBF8/7ihVR/6AiTdgIAADQ6u92u\n",
       "6dNf0E03/V533vm6brzxLm3fvt15kiEjAICL5BvFixMn7VyxQqquNi4LAACAF1q+fLk+/niHQkPf\n",
       "VocOs3Xw4F164okXJYdDWrzYeRHFCwDABfKN4kVcnNS9u3O/slJavdrQOAAAAN6msLBQdvtl8vNr\n",
       "I0kKCblSO3YUSps3S7t3SxaLcy4yAAAugG8UL6T6vS8YOgIAANCounXrJj+/r1Rbe1iSVFa2SL16\n",
       "dXcPGRk50jkXGQAAF8A3ixdM2gkAANCohgwZorS0ISor+7kOHrxNsbEZev75x5jvAgDQKMxGB2g2\n",
       "J644smaNdPiwFBJiXB4AAAAvYjKZ9NBD9+nnPx+niooKRUVFKcBmk774wnnBiROoAwBwnryueJGf\n",
       "v0NW63BXOzIyWNnZGVJYmNS/v/TNN5LNJi1fLo0ZY2BSAAAA7xMaGqrQ0FBnY/ly6ehRqV8/55wX\n",
       "AABcIK8rXthsZlksWa72mjVdXMWMR/ce0N11J5YupXgBAADQlBgyAgBoJF5XvDjZicWMH1plSqUp\n",
       "zhNM2gkAANC0KF4AABqJ70zYKenb9kNVreOzXH/3nVRcbGwgAAAAb1VS4hyu26aNdPXVRqcBALRw\n",
       "PlW8qPJvp41tT5ikc9ky48IAAAB4s7pertdc4yxgAABwEXyqeCFJX7Xr6G6wZCoAAEDTYMgIAKAR\n",
       "+V7xIvCE4sWSJZLDYVwYAAAAb+RwSIsXO/dHjjQ2CwDAK/hc8eK7tsFSUJCzsWuXtH27sYEAAECz\n",
       "yczMVGJiohISEjRz5swzXvf111/LbDbrP//5TzOma5kqKyu1a9cuHT161H3w+++lPXucy6P27m1c\n",
       "OACA1/C54kWtyc859rIOQ0cAAPAJNptNU6ZMUWZmpjZv3qw5c+Zoy5Ytp73ud7/7nW644QY56KHZ\n",
       "oBUrvtQ110zUT37yhJKTJ+qrr1Y7T5w4ZMRkMi4gAMBr+FzxQpI0YoR7nyVTAQDwCTk5OYqPj1dc\n",
       "XJwCAgI0ceJELViw4JTrXnvtNY0bN07h4eEGpGw5ysrK9KtfvSA/vxcVGvqeHI7n9fDDM1RRUcF8\n",
       "FwCARmc2OoAhrrvOvZ+VJdntkp9v1nEAAPAVRUVFio2NdbVjYmK0Zs2aU65ZsGCBli1bpq+//lqm\n",
       "M/QamDZtmms/OTlZycnJTRHZoxUVFclmu0TBwT0kSe3a9VJZWZj27NyphC++cF504i+MAAA+KTs7\n",
       "W9nZ2Rf9Pr5ZvOjdW4qIkPbulQ4ckDZulAYMMDoVAABoQmcqRJzokUce0YwZM2QymeRwOM44bOTE\n",
       "4oWvioyMlLRbx44VqXXraFVV7ZLJtFdR27dLVVVS//5SZKTRMQEABju5yD99+vQLeh/fLF6YTM7e\n",
       "F3PmONtLllC8AADAy0VHR6ugoMDVLigoUExMTL1r1q1bp4kTJ0qS9u/fr4ULFyogIECpqanNmrUl\n",
       "CAsL0/Tp9+nppx9UVVWcHI48Pf/8FAVlHZ9PjCEjAIBG5JvFC6l+8WLpUum3vzU2DwAAaFJJSUnK\n",
       "zc1VXl6eLrnkEs2dO1dz6p4FjtuxY4dr/6677tJPfvITChcNSE29UYMHJ2n37t2Kjo5WRESE9Nyz\n",
       "zpM+OJQGANB0fLd4ceIYzOXLpWPHpNatjcsDAACalNls1uzZszVq1CjZbDbdfffdslqtSk9PlySl\n",
       "paUZnLBlioyMPD6ERFJNjbR+vXN/0CDjQgEAvI7vFi+6dJG6d5e2b5eOHpVWr66/hCoAAPA6KSkp\n",
       "SklJqXfsTEWLN998szkieZfvv3c+V3XvLnXqZHQaAIAX8e0lNk7sfbF0qXE5AAAAvEHd6i2DBxub\n",
       "AwDgdXyueJGfv0NW63BZrcP1yCcr3CeWLDEuFAAAgDfIyXF+ZcgIAKCR+dywEZvNLIslS5K0s9N+\n",
       "aXe480ROjnT4sBQSYmA6AACAFoyeFwCAJuJzPS9OdDggTNuCji+RarNJX3xhbCAAAICWqrxc2rxZ\n",
       "CgiQ+vc3Og0AwMv4dPFCktZ3vM61//bkB2S1DldyMkuiAQAAnJe1ayWHQ+rXT2rTxug0AAAv4/PF\n",
       "i3Ud3ZN2Dq3uIIslSyUl5QYmAgAAaIGY7wIA0IR8bs6Lk33X/mpVS2olqduR79SxuljFRocCAADw\n",
       "UNu3b9fGjRsVEhKia665RgEBAc4TdfNdULwAADQBny9eVPm302pTGw1zVEmSLju4TFsMzgQAAOCJ\n",
       "vvzySz300EuqrR0mh2OXkpI+0euvv+gsYNT1vGCyTgBAE/D5YSOStMyvrWt/YOnnBiYBAADwXM88\n",
       "81cFBDyrsLBHFBb2F61da1ZWVpZUVOTc2reXevQwOiYAwAtRvJC02OQuXlx5IEMBDruBaQAAADxT\n",
       "aWmZ2rTpKkkymUySuurQoUPuXhcDB0p+PF4CABoff7tIWmtqreI2XSRJwbVlGnLkoMGJAAAAPM/Q\n",
       "oZfrwIHXZbdXqbLyB/n7Z6lfv35M1gkAaHIULyTJZFJW+HhXc/ThvQaGAQAA8EzPPfeYhg/fq4MH\n",
       "U9W69ZN6+eUp6tGjh3uyTua7AAA0EZ+fsLNOdsQETSp4QZJ0bcV+qaqKNcoBAABOEBISotmz/ySH\n",
       "w3F82Igkm01au9a5T88LAEAToefFcduCLlNRm26SpGC7TfqciTsBAABOx1W4kKStW6XycqlzZ8li\n",
       "MS4UAMCrUbyoYzIpK2KCuz1vnnFZAAAAWgrmuwAANAOKFyfIjnDPe6GMDOnoUePCAAAAtATMdwEA\n",
       "aAYUL06wvV0/7Wp7fG3yigpp4UJjAwEAAHg6el4AAJoBxYsTnTx0ZO5c47IAAAB4uqNHpU2bJD8/\n",
       "6fLLjU4DAPBiFC9OUm/oyKefSkeOGBcGAADAk61f71xtpHdvqV07o9MAALwYxYuT5LXrrdxWgc5G\n",
       "ZaX0v/8ZGwgAAMBTMWQEANBMKF6cRmZIhLvB0BEAAIDTY7JOAEAzoXhxGpnB4e7GZ5851y4HAABA\n",
       "ffS8AAA0E4oXp5FVXKIfWh8ft1lVpT8MusbYQAAAAJ5m3z5p507nXBeXXmp0GgCAl6N4cRo2m1kr\n",
       "Lvm9q31l4S4D0wAAAHigul4Xl18u+fsbmwUA4PUoXpxBdrh71ZGhR0qlQ4cMTAMAAOBhmO8CANCM\n",
       "KF6cQVFggrYFDZAktXI4pAULDE4EAADQ/LKysnXHHb/W7bf/SkuXLnOfYL4LAEAzonjRgKyICe7G\n",
       "vHnGBQEAADDAihVfaurUv+u778bp++/H65FH/qkvvlguORzu4gU9LwAAzYDiRQO+CL/V3Vi0SDp4\n",
       "0LgwAAAAzeyjjxbJ3/9etW9/pdq3HyJ///s0b94i6ccfnc9FFosUE2N0TACAD6B40YA9bbtpS/BA\n",
       "Z6OmRpo/39hAAAAAzahVK7NstqOutt1+VK1bm+v3ujCZDEoHAPAlZy1eZGZmKjExUQkJCZo5c+Yp\n",
       "57du3aohQ4aoTZs2+stf/nJer20JsiPcE3dq7lzjggAAADSzO++8RWbzv7R370fat+9j+fu/oTvv\n",
       "vMU9WSfzXQAAmkmDxQubzaYpU6YoMzNTmzdv1pw5c7Rly5Z613Tq1EmvvfaaHn300fN+bUtQb+jI\n",
       "kiXS/v3GhQEAAGhGvXv31gcfPK9Jk3Zp/Pg8vffec+rbty+TdQIAml2DxYucnBzFx8crLi5OAQEB\n",
       "mjhxohactOpGeHi4kpKSFBAQcN6vbQlK2nTRN21CnA2bTfrvf40NBAAA0IysVqueeuo3evrpR3Xp\n",
       "pZdKx45JGzY4Tw4caGw4AIDPMDd0sqioSLGxsa52TEyM1tR1EzyLc31tcfEKlZVNkyTZ7YfO6b2b\n",
       "28KQCPWvOuxszJ0r3XuvsYEAAD4rOztb2dnZRseAL9u0SaqulhITpfbtjU4DAPARDRYvTBcxAdO5\n",
       "vtZiGaoOHaZJkoqLl17w92tKnweH6/d7f3Q2srKkvXuliAhjQwEAfFJycrKSk5Nd7enTpxsXBr6p\n",
       "7pdRLJEKAGhGDQ4biY6OVkFBgatdUFCgmHNcDutiXutpSgJaS1df7WzY7dL/+3/GBgIAADAK810A\n",
       "AAzQYPEiKSlJubm5ysvLU3V1tebOnavU1NTTXutwOC74tS3ChAnufVYdAQAAvoqeFwAAAzQ4bMRs\n",
       "Nmv27NkaNWqUbDab7r77blmtVqWnp0uS0tLSVFxcrIEDB+rw4cPy8/PTrFmztHnzZgUFBZ32tS3W\n",
       "2LHS1KmSwyEtXy7t2SNFRRmdCgAAoPkcPCht2ya1bi316WN0GgCAD2mweCFJKSkpSklJqXcsLS3N\n",
       "tW+xWOoNDznba1usqCjpmmuk7GxnAePjj6WHHjI6FQAAQPNZu9b59bLLpFatjM0CAPApDQ4bwUnG\n",
       "j3fvz5tnXA4AAAAj1A0ZYb4LAEAzo3hxPsaOlfyO/yf78kupsNDYPAAAAM2pbrJO5rsAADQzihfn\n",
       "IyJCGj7c3f7oI+OyAAAANCeHg54XAADDULw4B/n5O2S1DpfVOlz/9/0J83swdAQAAPiKXbukvXul\n",
       "Tp2kbt2MTgMA8DFnnbATks1mlsWSJUna1Gm/aosjZJZDWr1ays+XunQxOCEAAEATO7HXhclkbBYA\n",
       "gM+h58V5OhwQpq/adXQfeP1148IAAAA0l7r5LhgyAgAwAMWLC/Bx+yh3Iz1dqqoyLgwAAEBzqOt5\n",
       "wWSdAAADULy4AEuDw6TOnZ2N/fulDz4wNhAAAEAj2b59ux588AmNH/+g/vGPf6u2tlay2aT1650X\n",
       "DBxobEAAgE+ieHEBbCaTNGWK+8CsWc4ZuAEAAFqwkpIS3Xbbo1qx4grt3JmmV1/drBdf/KuUlydV\n",
       "VkrR0VJYmNExAQA+iOLFhbrnHikw0Lm/aZOUnW1oHAAAgIv11Vdfqbz8SnXqlKqgoL7q1OkpzZv3\n",
       "ufT9984LevUyNiAAwGdRvLhQHTtKd9zhbs+aZVwWAABwTjIzM5WYmKiEhATNnDnzlPPvv/+++vXr\n",
       "p759++qqq67Spk2bDEhpHLPZLJPpqKtts1UqICBA2rzZeeDSSw1KBgDwdRQvLsbUqe79jAxpxw7j\n",
       "sgAAgAbZbDZNmTJFmZmZ2rx5s+bMmaMtW7bUu6Zbt25avny5Nm3apP/7v//TfffdZ1BaYwwbNkxR\n",
       "UVu0d+/fdODAZzp06Ck98MB4d/GCnhcAAINQvLgYVqt0/fXOfYdDmj3b2DwAAOCMcnJyFB8fr7i4\n",
       "OAUEBGjixIlasGBBvWuGDBmi9u3bS5IGDx6swsJCI6IaJiQkRB9++Ffdd59Jqamb9NJLk3THHT9z\n",
       "Dxuh5wUAwCBmowO0eA8/LC1a5Nz/17+k6dOl4GBjMwEAgFMUFRUpNjbW1Y6JidGauuU/T+Nf//qX\n",
       "Ro8efdpz06ZNc+0nJycrOTm5sWIaLjQ0VA8/fL/7gN0u1fVQsVqNCQUAaLGys7OV3QhzRFK8uFg3\n",
       "3CD16CFt2yYdPiy9/Xb9lUgAAIBHMJlM53xtVlaW/v3vf2vlypWnPX9i8cLr5eVJR49KUVHOOb8A\n",
       "ADgPJxf5p0+ffkHvw7CRi+XnV3/ui1dfdf6GAgAAeJTo6GgVFBS42gUFBYqJiTnluk2bNunee+9V\n",
       "RkaGOvKPdSbrBAB4BIoXjWHyZOn4+Fjl5kqZmcbmAQAAp0hKSlJubq7y8vJUXV2tuXPnKjU1td41\n",
       "u3bt0i233KL33ntP8fHxBiX1MEzWCQDwABQvGkNQkHT33e42y6YCAOBxzGazZs+erVGjRqlXr16a\n",
       "MGGCrFar0tPTlZ6eLkl69tlndfDgQd1///0aMGCABg0aZHBqD8BknQAAD8CcF41lyhTplVecQ0YW\n",
       "LXL+loLfUAAA4FFSUlKUkpJS71haWppr/4033tAbb7zR3LE8Gz0vAAAegJ4XjaVrV+mmm9ztV181\n",
       "LgsAAEBjsNspXgAAPALFi8b08MPu/XfekUpLjcsCAABwsXbtkiorJYtFCg01Og0AwIdRvGhMw4ZJ\n",
       "/fo5948eleh2CgAAWjJ6XQAAPATFiwuQn79DVutw15acfHymcpOpfu+L2bOl2lpjQgIAAFwsJusE\n",
       "AHgIihcXwGYzy2LJcm0lJeXuk5MmSeHhzv2CAmn+fGNCAgAAXCx6XgAAPATFi8bWpo30y1+628eX\n",
       "TU1OTj19bw0AAABPVdfzguIFAMBgFC+awv33SwEBzv0vv5TWr1dJSfmZe2sAAAB4GofD3fOCYSMA\n",
       "AINRvGgKUVHS+PHu9vHeFwAAAC1GQYF05IgUESF16mR0GgCAj6N40VROnLhzzhyF1VYblwUAAOB8\n",
       "MVknAMCDULxoKgMHSkOGOPdrajShbLexeQAAAM7A4XDoyJEjcjgc7oNM1gkA8CAUL5rSCb0vJh4s\n",
       "UoD9mIFhAAAATrVlyxaNGDFRgwaN0zXXjNPGjRudJ5isEwDgQSheNKVbbpFiYiRJYbYaDd871+BA\n",
       "AAAAblVVVbr33qd08OBURUQsVGXl7/XLX07X4cOHmawTAOBRKF40AdeyqH2v11+OtXIdH1f4skwO\n",
       "u4HJAAAA3IqKilRREaL27a+SJAUHJ6mqyqJd+fkMGwEAeBSKF03gxGVRl/fIUZVfW0lSQsU39L4A\n",
       "AAAeIzQ0VA7HftXU7Jck1daWyWbbrfBjx6Tycik83LkBAGAwihdN7HBAJ/0nZqqrfe/O3yvAXmVg\n",
       "IgAAAKeOHTvq8cfvUHn5Ayot/YMOHfqlpk69RZEHDjgvoNcFAMBDmI0O4As+6Px7jdz1gsJll6Uq\n",
       "X2MLX9Urrc7+OgAAgKY2adKtuvzyfsrLy1Ns7DhZrVbppZecJyleAAA8BD0vmsERc3s959/R1f55\n",
       "/h/VsbbawEQAAABuPXr00PXXX+8sXEhM1gkA8DgUL5rJG34h2hXYU5IUZDusB/fnG5wIAADgDFgm\n",
       "FQDgYSheNJNak0n/6PaCqz2hbLf0ww8GJgIAADgNh4OeFwAAj0PxohHk5+9wLo16fMvPLzztdV91\n",
       "GqMNHZIlSWY5pMcea8aUAAAA52D3bunwYalTJ1YaAQB4DIoXjcBmM7uWRrVYsmSz2U9/ocmkv3f/\n",
       "i+wyOdsZGVJ2drPlBAAAOKsTh4yYTMZmAQDgOIoXzSw3+DItjrzdfeA3v5HsZyh2AAAANDeGjAAA\n",
       "PBDFCwO80e2PqjId/0+/fr30/vvGBgIAAKjDZJ0AAA9E8cIA+1vH6M3QWPeBJ56QKiuNCwQAAFCH\n",
       "nhcAAA9E8cIgb4TGSpGRzkZhofTyy8YGAgAAOHGlEXpeAAA8CMULg1T6m6Vnn3UfmDFDKi42LhAA\n",
       "AMCePVJZmRQa6v4lCwAAHoDihZF+8Qv3bzUqKvSh9XLXcqvJyanGZgMAAL7nxF4XrDQCAPAgFC+M\n",
       "ZDZLL77oat5aVqwrgmfLYslSSUm5gcEAAIBPYrJOAICHonhhtBtukEaOlCT5y6607b81OBAAAPBZ\n",
       "TNYJAPBQFC+MZjJJL74o+/HmFaULdXnpYkMjAQAAH8VknQAAD0XxwhP07av/tLe4mr/c/qj8HA4D\n",
       "AwEAAJ/jcLiHjdDzAgDgYSheeIhXw7rqqF+gJCn+yCb99BArjwAAgGZUUiIdPCh16CBZLGe/HgCA\n",
       "ZmQ2OoCvys/fIat1uLu9e58+7PyY7sqbJkl6eP9OqaJCCgoyKCEAAPApJ07WyUojAAAPQ88Lg9hs\n",
       "ZlksWa7NZrNrXuyj2t8qSpIUUVstPfecwSkBAIDPYLJOAIAHo3jhQar82+nfXd0FC/vMmbq9ywBZ\n",
       "rcOVnJxqYDIAAOD1mKwTAODBKF54mEzLnVrbcYQk54fzl5L9iu/0H5WUlBsbDAAAeI3c3Fx9+OGH\n",
       "+vTTT1VVVeU8yGSdAAAPRvHCwzhMfpqR+Lb2H/9oIo4V6jfb7nPOAA4AAHCRVq1apVtvfUx/+MMB\n",
       "Pf74V7r99qmqOnq0/pwXAAB4GIoXHuhA60uUZg53tZP3faxbWH0EAAA0gmef/YfM5qcVEfGgwsKe\n",
       "0+bNkcqeN08qLZVCQqRLLjE6IgAApzhr8SIzM1OJiYlKSEjQzJkzT3vN1KlTlZCQoH79+mnDhg2u\n",
       "43Fxcerbt68GDBigQYMGNV5qH/CpXztlXJLmaj9R8qO0bdtFvWdycqqs1uGujXk0AADwPWVl5WrT\n",
       "JlaSZDKZ5HDEym/rVufJSy9lpREAgEdqsHhhs9k0ZcoUZWZmavPmzZozZ462bNlS75rPPvtMP/74\n",
       "o3Jzc/XPf/5T999/v+ucyWRSdna2NmzYoJycnKa5Ay/2t+4vKT8wUZLUzmGTfvYzqbr6gt+vpKS8\n",
       "3gonzKMBAIDvue66gSotTVdtbZmOHNkss/lz9fH3d55kyAgAwEM1WLzIyclRfHy84uLiFBAQoIkT\n",
       "J2rBggX1rsnIyNDkyZMlSYMHD1ZZWZlKSkpc5x3M1XDBjvkH6g+95qja1Mp5YN066emnjQ0FAABa\n",
       "tCeffEQ33SRVVd2u4OA/6JVXpiiqtNR5ksk6AQAeytzQyaKiIsXGxrraMTExWrNmzVmvKSoqUmRk\n",
       "pEwmk0aMGCF/f3+lpaXp3nvvPeV7FBevUFnZNEmS3X7oYu7FK20P6q83uj2vB7b/xnngz3+WRo2S\n",
       "hg83NhgAwBDZ2dnKzs42OgZasMDAQD3//JN6/vkTDj473fmVnhcAAA/VYPHCdI5jHs/Uu+LLL7/U\n",
       "JZdcon379mnkyJFKTEzU0KFD611jsQxVhw7TJEnFxUvP6fv5mo9jHlHf4ud09ZGDzlVHbr9d2rhR\n",
       "6tTJ6GgAgGaWnJys5ORkV3v69OnGhYH3YKURAICHa3DYSHR0tAoKClztgoICxcTENHhNYWGhoqOj\n",
       "JUmXHJ+tOjw8XDfffDPzXlwgh8lPv49KlMLCnAeKiqR772X5VAAAcPH27ZP275eCg6WTnvMAAPAU\n",
       "DRYvkpKSlJubq7y8PFVXV2vu3LlKTa2/QkVqaqreeecdSdLq1avVoUMHRUZGqrKyUuXlzgkhg3eS\n",
       "XAAAGkBJREFUjxw5okWLFqlPnz5NdBveb7+5tfTmm+4D//2v9MYbxgUCAADeYfNm59devVhpBADg\n",
       "sRocNmI2mzV79myNGjVKNptNd999t6xWq9LT0yVJaWlpGj16tD777DPFx8erXbt2evP4P7CLi4t1\n",
       "yy23SJJqa2v185//XNdff30T346XGzNGeuAB6W9/c7YfeUQaOlRKTDQ2FwAAaLnqhowwWScAwIM1\n",
       "WLyQpJSUFKWkpNQ7lpaWVq89e/bsU17XrVs3ffPNNxcZD6d48UUpO9v5W5LKSufyqV99JbVubXQy\n",
       "AADQEp3Y8wIAAA/V4LAReKC2baU5c9zFig0bpKeeMjYTAAAtRGZmphITE5WQkKCZM2ee9pqpU6cq\n",
       "ISFB/fr104YNG5o5oQGYrBMA0AJQvGiJ+vaVTnzgevFFackS4/IAANAC2Gw2TZkyRZmZmdq8ebPm\n",
       "zJmjLVu21Lvms88+048//qjc3Fz985//1P33329Q2mZU1/OCYSMAAA9G8aKlmjpVuuEGd/uOO6Td\n",
       "u43LAwCAh8vJyVF8fLzi4uIUEBCgiRMnasGCBfWuycjI0OTJkyVJgwcPVllZmUpKSoyI2zz275f2\n",
       "7pWCgqTYWKPTAABwRmed8wIeymSS3npL6tPHucTZnj3SqFHSF19IoaFGpwMAwOMUFRUp9oR/oMfE\n",
       "xGjNmjVnvaawsFCRkZH1rps2bZprPzk5WcnJyU2Sucmx0ggAoIllZ2crOzv7ot+H4kULkZ+/Q1br\n",
       "cFc7MjJY2dkZ0vvvS6NHS7W10nffOVckWbxYatfOwLQAAHge0zn+49zhcJz1dScWL1o0JusEADSx\n",
       "k4v806dPv6D3oXjRQthsZlksWa72mjVdXMWMG8MT9OKe42N2v/pKuvVWacECKSDAiKgAAHik6Oho\n",
       "FRQUuNoFBQWKiYlp8JrCwkJFR0c3W8Zmd9tt0oABUmCg0UkAAGgQc160UHXFDIslS+t6btar8a+6\n",
       "Ty5cKN15p2S3G5YPAABPk5SUpNzcXOXl5am6ulpz585VampqvWtSU1P1zjvvSJJWr16tDh06nDJk\n",
       "xKsEBUmDBzuHoQIA4MEoXniJ/8Y8pD+ZQ9wHPvhA/69zvHRS11cAAHyV2WzW7NmzNWrUKPXq1UsT\n",
       "JkyQ1WpVenq60tPTJUmjR49Wt27dFB8fr7S0NP3tb38zODUAAJAYNuJVpps66dJLfqabdv9DkjS2\n",
       "aKdmRXTTP8LiJEn5+YWyWAwMCACAwVJSUpSSklLvWFpaWr327NmzmzMSAAA4B/S88CYmk15NmK2s\n",
       "8PGuQw/vz9N9tvGyWLJkszGMBAAAAADQ8tDzwsvYTf563vqOgmoPauDBxZKkh3Mf1OGATlplcDYA\n",
       "AAAAAC4EPS+8UI1faz3d+z/KMbWWJPnJoSe23KYR9kqDkwEAAAAAcP4oXnipKv8g/dRsUX5goiQp\n",
       "wFGjebUlsh5eY3AyAAAAAADOD8ULL3bA5K/f9l2kktaxkqR2cuj5TaPV5chmg5MBAAAAAHDuKF54\n",
       "uX1tYvXbfot0KKCTJKl9bale2HS9IqvyDU4GAAAAAMC5oXjhAwoCE/W7PgtVIZMkKfxYkV755hrF\n",
       "HzticDIAAAAAAM6O4oWP+CFkoG41R6ra1EqSZKnK15z89VJmpsHJAAAAAABoGMULH7LML1BP9/6v\n",
       "jvq3kyQF2W3SjTdKf/2rwckAAAAAADgzihc+Zk2n0XpowErXJJ6y26UpU6SpU6XaWmPDAQAAAABw\n",
       "GhQvfND2oH564LI12tQm2H3wtdek1FTp8GHjggEAAAAAcBoUL3xUaesoTe7cXxo3zn1w4ULpqquk\n",
       "fFYiAQAAAAB4DooXPqzKz1+aO1d64gn3we++kwYPltasMS4YAAAAAAAnoHjhw/Lzd8h66XWy/meV\n",
       "Ho9KVI3JuZSqSkqk5GRp3jxD8wEAAAAAIFG88Gk2m1kWS5Ysliyt6blFv4jtJ4WGOk9WVUkTJkjP\n",
       "PSc5HMYGBQAAAAD4NIoXcFkb2ME5XKRnT/fB//s/afJk6ehR44IBAAAAAHwaxQvUFx8vffWVdO21\n",
       "7mPvvisNGCCtWmVcLgAAAACAzzIbHQAeqGNHKTNTevBB6fXXncd++EG6+mp9dEmc/tQuxjnZp6TI\n",
       "yGBlZ2cYGBYAAAAA4O3oeYHTCwiQ0tOlf/5TCg52HnM4dGvRTn1asFuj2kyTxZKlkpJyY3MCAAAA\n",
       "ALwexQucUfLwm2R96QNdG3GpVrQLdR2PPrpdr3yTrKm5UxRotxmYEAAAAADgCxg2gjMqKSmXxZIl\n",
       "h6SnYxy6ofgtpf1wjzrILkm6ueivGmDy112d+2t1u46SGEYCAAAAAGh89LyAS37+Dlmtw11bfn6h\n",
       "+6TJpMyouzQgIEarOo1xHY5z2PRmwUb9+VAPdQ+bzzASAAAAAECjo3gBF5vNLIsly7XZbPZTrtlt\n",
       "MuvJ3hn6o/VdHTZ3dB3/yZ5/6t9f99bVFaXNGRkAAAAA4AMoXuD8mUxaEnmb7hy0WfNNga7DEccK\n",
       "9XrhJun226W8POPyAQAAAAC8CsULXLCDrSyaYI7U9F4fqiwgzH3ivfekHj2kBx6QioqMCwgAAAAA\n",
       "8AoUL3BxTCZlR0zQnQM3Kyt8vPt4TY3097+rOraz9KtfSSUlxmUEAAAAALRoFC/QKA61Ctezl87V\n",
       "SHOUvm1/let4K4ddeuUVqVs36fHHpQMHDEwJAAAAAGiJKF6gUS33a6up/Vfot30ztTU4yX2islKa\n",
       "OVNHIi3SM89Ihw4ZFxIAAAAA0KJQvEDjM5m0NnSU7r8sR7eYI/Vju76uU+1stdKzz0pdu0p/+pNU\n",
       "UWFgUAAAAABAS0DxAk3HZNL//NrpvqQNmtZrnvIDE93nDh6UnnzSOZxk+nSpsNC4nAAAAAAAj0bx\n",
       "Ak3OYfLTFxG36hcDv9NjUVape3f3yX37pGnTpC5dpNRU6X//k2w2w7ICAAAAADwPxQs0G7vJX5+0\n",
       "j5S2bJHeeEPq3PmEk3bpk0+kMWOcQ0qefdbVGyM5OVVW63DXlpycatAdAAAAAACMYDY6AHxLfv4O\n",
       "WfteL0kKaBunsdYwPRPVQVq2zH1RQYFzUs/p06UxY9Rze578u2+Q3eQvSSouHm5EdAAAAACAQeh5\n",
       "gWZls5llsWTJYslSp6gv9KEjRFq6VPrhB+m3v5XCwtwX2+1SRobSC7/VB6u76o68ZxV2rMi48AAA\n",
       "AAAAQ1C8gGfo0UP685+dQ0U+/FAaXr93ReSxAt2V94zmfhWr9/PXSy+8IOXmSmJYCQAAAAB4O4aN\n",
       "wLO0bi1NmODctm2TXn9dpS/PUqitRpLkJ4cuO3pYeuwx59arlyaWVGhjl4/0Q3CSHCY/rVnTRVar\n",
       "u/gRGRms7OwMo+4IAAAAAHCRKF7Ac/XoIb3wgpIzcjTOfL/G7H5d/cqy5S+7+5rNm/VLSTowWPta\n",
       "XaKVYTfp9ZpqVUd8rlq/VpJ0SjFDOrWgkZycqpKS8jOeBwAAAAAYh+IFPM7JhYT8gt3KGjxRWRET\n",
       "FVKzX712DNXzg3pKixZJR4+6rguv3q2f7v67fiqpYmW41nQarTWho1VY65DFklXve5w86WdJSXm9\n",
       "a5gUFAAAAAA8B8ULeJyTCwk7dnR37R8OCNP89hY9P3++VFkpLV6s/0z+pa6rrFH7mgOu64Jsh3Xd\n",
       "3g913d4P9YSk4q+6aGOHa7SpwzBtaj9MxQ5Hc94SAAAAAOAiULxAi5Ofv6PeMJD86iANuXKLeh9a\n",
       "pav2z1dS4Wvqptp6r7Ec2yVLybsaVfKuJGmffytp/Hhp2DBp2DCZKGYAAAAAgMeieIEWp2651To7\n",
       "dnSX3WR29qroMEyrSubrtn7zNeTAp+pX9oWsBxcrSPWLE+G2aumjj5ybpFV+Zn2/P1XbgpP0Y1B/\n",
       "raqpkhwOyWRq1nsDAAAAAJyK4gW8j8mkHUF9tSOor97v8oRyVnbTHX0+VN9Dy9W3bLn6Hlqh4Nqy\n",
       "ei/pYK/VVQc+0VUHPnEfDA+X+vd3bwMGSD17SmYzE3wCAAAAQDOieAGvV2syaWvIIG0NGaR5sY/K\n",
       "5LArOH+wFvxmsvTFF9Ly5dLevae+8MABaelS51anTRupTx89sK1QeyKeUGHbHioI7KFvi+8871wU\n",
       "QAAAAADg3FC8gM9xmPy0rU2QNGWKc3M4lNL9Cl3T+n7FV3yj+PIN6l6+UsF226kvrqqSvv5a4yXp\n",
       "0EOuw8dMflLv3lJCgnOJ1x499NBr/9Y3R6T9/gGSyaQ9e/IVFdXF9Zr8/EINHpzrarPCCQAAAACc\n",
       "HsULGOrkyTedxwplsTRjCJNJea0DVWW5U58fP7RmdWddecklsh6rkLWqQnEH9ykpIFQRxwpP+xat\n",
       "HXbp+++d23GvHf96xD9YhYE99F3FXtmCf6p9rWNV0qazltZMVeixPTrYKlIOk1/T3uMZ0PsDAAAA\n",
       "QEtA8QKGOnnyTan+0qhGsdkDZOu8Wt9J+k7SqlXddeWQ7WpfvU/dj2xUwHcTNCz8JsUczVVM5TaF\n",
       "1pxm2Mlx7Wzl6lm+Tj0lqfBl1/FnJemrS1RjCtC+1jEqMpVKt98uxcY6N4tFioiQIiOlyEglj/mZ\n",
       "SvZWuF7fGIWGk5elpfcHAAAAAE9E8QI+6ZTlVs+xt8ehVuFa32qEVvl30JrEf7uOVxQN1dcfvCxt\n",
       "2+bccnP17X8+Udcak4Jshxt8zwBHjS6p2qlLJOm998543UKTn8pad9bBgAgdbBWpH3KX6e9hcTrg\n",
       "H6BScysd8jfLHN5e6R+9JYWGSiEhkp8xPToAAAAAoDFRvGgGZWXZRkdoNnb7UaMjnJPTLbd6Pk6+\n",
       "zwp/s5SU5NyOG28dLkvkMnWo2aeYo9t0aNNYXdXl14qs2qXwYwVqV/q5uvoHqX1t6Tl9z7YOu9pW\n",
       "5SmqKk+SdJUkHThS/6ICSd2P34ufn9Shg7OQcfLWvr0UEqIJB3fLbHpflf4hqjSHqGNVubR9u7Pw\n",
       "ERys/oOv1bHq1vW+xcX2+PDUoSrZ2dlKTk42OkaT4z4BnMybfl686V4k7sfTcT+ezZvux5vu5WKc\n",
       "tXiRmZmpRx55RDabTffcc49+97vfnXLN1KlTtXDhQgUGBuqtt97SgAEDzvm1vsCXihcOR5XREZrF\n",
       "Od+nyaSyVhEqaxWhVf5BKujs/hlYtaq7rrxyu9rYjij8WIFKvxmmfqGhiqo9JkvNMUWZ7bqqexep\n",
       "pMS5VZ3nf1u7XSotdW5nME2SSm6rfzA+3rX7E0mPmkNV5d/OtR3O3yCNHi21aycFBjq/nrgFBjpX\n",
       "ZWnb1vn1xP22bRW4q0T9Iueq2q+tqv3aqGBPqjOrwb1EfOUvBe4Tvqq0tFQTJkxQfn6+4uLiNG/e\n",
       "PHXo0KHeNQUFBbrjjju0d+9emUwm3XfffZo6dapBiZuPN/28eNO9SNyPp+N+PJs33Y833cvFaLB4\n",
       "YbPZNGXKFC1ZskTR0dEaOHCgUlNTZbVaXdd89tln+vHHH5Wbm6s1a9bo/vvv1+rVq8/ptYC3uJiJ\n",
       "R6v826kgMFGrFKwjiVtdx9es6aIuhwOltl2lLnEqzS/QyL6Z6lizVx2rS3Rwa5ouj31QHatLFFJz\n",
       "QCG1pfIrW6Go1lEKrilVO1t5A9/13PhLal9bemrvkIULL/g9P5OknV1P+kb+qpFJ1SY/1ZhMqnI4\n",
       "ZPM3q8bkpxqTn47U1kit2qjaz0+1MsmvTYCuuPoKKSDg9FurVu79YcOkkSPPO6en9hABcGFmzJih\n",
       "kSNH6rHHHtPMmTM1Y8YMzZgxo941AQEBevnll9W/f39VVFTo8ssv18iRI3l2AQDAAzRYvMjJyVF8\n",
       "fLzi4uIkSRMnTtSCBQvq/SWekZGhyZMnS5IGDx6ssrIyFRcXa+fOnWd9LeAtmmLi0VOGtuzsrqLA\n",
       "BBUpQZK0Kve3ujJuWr3XrFrVXVdesV2S5G+v0ZavEnTdgM8VXFOq4NpSlWy+S5d1fVLtag8r0HZY\n",
       "h4vS1S1sjNrZDiuw9rB0eLVCzf4KstvUzlYryXFR93A+AuRQgMPm/pa1Jy1VW1Xt3q+UlHGOhYTH\n",
       "H1fyH1+rV4iQzl6MaI7JTM+3QHLy9efyGrhRkPJtGRkZ+uKLLyRJkydPVnJy8inFC4vFIsvxqnNQ\n",
       "UJCsVqt2797NswsAAJ7A0YCPPvrIcc8997ja7777rmPKlCn1rhkzZoxj5cqVrvZ1113nWLt2rePj\n",
       "jz8+62vl/GcKGxsbGxsb20VsOLsOHTq49u12e7326ezcudPRuXNnR3l5+SnnjP682djY2NjYWvp2\n",
       "IRrseWEymRo67eL8e/z8XejrAAAATjZy5EgVFxefcvyPf/xjvbbJZGrwGaeiokLjxo3TrFmzFBQU\n",
       "dMp5nl8AAGh+DRYvoqOjVVBQ4GoXFBQoJiamwWsKCwsVExOjmpqas74WAACgsSxevPiM5yIjI1Vc\n",
       "XCyLxaI9e/YoIiLitNfV1NRo7Nixuu222/TTn/60qaICAIDz1OD0/klJScrNzVVeXp6qq6s1d+5c\n",
       "paam1rsmNTVV77zzjiRp9erV6tChgyIjI8/ptQAAAM0hNTVVb7/9tiTp7bffPm1hwuFw6O6771av\n",
       "Xr30yCOPNHdEAADQgAaLF2azWbNnz9aoUaPUq1cvTZgwQVarVenp6UpPT5ckjR49Wt26dVN8fLzS\n",
       "0tL0t7/9rcHXAgAANLfHH39cixcvVo8ePbRs2TI9/vjjkqTdu3frxhtvlCStXLlS7733nrKysjRg\n",
       "wAANGDBAmZmZRsYGAAB1LmimjEawcOFCR8+ePR3x8fGOGTNmGBWjWXTp0sXRp08fR//+/R0DBw40\n",
       "Ok6jueuuuxwRERGO3r17u44dOHDAMWLECEdCQoJj5MiRjoMHDxqYsHGc7j6feeYZR3R0tKN///6O\n",
       "/v37OxYuXGhgwsaxa9cuR3JysqNXr16OSy+91DFr1iyHw+Gdn+mZ7tXbPtejR486Bg0a5OjXr5/D\n",
       "arU6Hn/8cYfD4X2f6Znu09s+zzq1tbWO/v37O8aMGeNwOLzv82wpvOXPl7c9j7XkZy5ve67ytucn\n",
       "b3tO8qZnIW973vHW55rGeH4xORzNP+uUzWZTz549tWTJEkVHR2vgwIGaM2eO1/bM6Nq1q9atW6fQ\n",
       "0FCjozSqFStWKCgoSHfccYe+/fZbSdJjjz2msLAwPfbYY5o5c6YOHjx4ylJ0Lc3p7nP69OkKDg7W\n",
       "r3/9a4PTNZ7i4mIVFxerf//+qqio0OWXX6758+frzTff9LrP9Ez3Om/ePK/7XCsrKxUYGKja2lpd\n",
       "ffXVevHFF5WRkeF1n+np7nPp0qVe93lK0ksvvaR169apvLxcGRkZXvn/3ZbAG/4e8MbnsZb8zOVt\n",
       "z1Xe9vzkbc9J3vYs5G3PO974XNMYzy8NDhtpKjk5OYqPj1dcXJwCAgI0ceJELViwwIgozcaAGlGT\n",
       "Gzp0qDp27FjvWEZGhiZPnixJmjx5subPn29EtEZ1uvuUvO8ztVgs6t+/vyQpKChIVqtVRUVFXvmZ\n",
       "nuleJe/7XAMDAyVJ1dXVstls6tixo1d+pqe7T8n7Ps/CwkJ99tlnuueee1z35o2fZ0vR0v98eevz\n",
       "WEv9XLztucrbnp+87TnJ256FvO15x9ueaxrr+cWQ4kVRUZFiY2Nd7ZiYGNcPizcymUwaMWKEkpKS\n",
       "9Prrrxsdp0mVlJQoMjJSknNm95KSEoMTNZ3XXntN/fr10913362ysjKj4zSqvLw8bdiwQYMHD/b6\n",
       "z7TuXq+44gpJ3ve52u129e/fX5GRkRo+fLguvfRSr/xMT3efkvd9nr/61a/0wgsvyM/P/de3N36e\n",
       "LUVL//Pljc9j3vbM5Y0/3y3950byvuckb3gW8rbnHW97rmms5xdDihcNra3ujVauXKkNGzZo4cKF\n",
       "+utf/6oVK1YYHalZmEwmr/2s77//fu3cuVPffPONoqKi9Jvf/MboSI2moqJCY8eO1axZsxQcHFzv\n",
       "nLd9phUVFRo3bpxmzZqloKAgr/xc/fz89M0336iwsFDLly9XVlZWvfPe8pmefJ/Z2dle93l++umn\n",
       "ioiI0IABA874mxdv+Tw9xciRI9WnT59TtoyMDK/48+WNf1a8+ZnLG36+veHnxtuek7zlWcjbnne8\n",
       "6bmmMZ9fDCleREdHq6CgwNUuKChQTEyMEVGaRVRUlCQpPDxcN998s3JycgxO1HQiIyNVXFwsSdqz\n",
       "Z48iIiIMTtQ0IiIiXD9k99xzj9d8pjU1NRo7dqxuv/121zKC3vqZ1t3rbbfd5rpXb/1cJal9+/a6\n",
       "8cYbtW7dOq/9TCX3fa5du9brPs9Vq1YpIyNDXbt21aRJk7Rs2TLdfvvtXv15Gm3x4sX69ttvT9lS\n",
       "U1O94s+XNz6Pedszl7f9fLf0nxtve07yxmchb3ve8YbnmsZ8fjGkeJGUlKTc3Fzl5eWpurpac+fO\n",
       "VWrq/2/vjnUMiKIwjh+Fh5DoJApy3cwrUKPVqLyAp5jCO5BMNDrdFDQSb+ABKBQUVILybLWyu1kb\n",
       "G2RmTv6/aqK6J5+Z+XJDbiuJpbzd5XKR0+kkIiLn81lms5k45xJe1fu0Wi2JokhERKIouj0Irdnt\n",
       "drfr6XRqIlNVlV6vJ5VKRfr9/u1zi5nem9VarofD4faTwuv1KvP5XIIgMJfpvTk/X4giNvIMw1C2\n",
       "261sNhuZTCZSr9dlPB6byzMrLDwvrPUxi53L2v2d5fvGWk+y1IWs9R1rveal/eWl55/8QxzHWi6X\n",
       "tVQqaRiGSS3j7dbrtXrv1Xuv1WrV1KydTkcLhYLm83ktFos6Go30eDxqo9HI3JFEf/k553A41G63\n",
       "q845rdVq2m63db/fJ73Mpy2XS83lcuq9/3YEk8VMf5s1jmNzua5WKw2CQL336pzTwWCgqmou03tz\n",
       "Wsvzq8Vioc1mU1Xt5ZkVVr5flvpY1juXtV5lrT9Z60mWupC1vmO51zzbXxI5KhUAAAAAAOBRifxt\n",
       "BAAAAAAA4FFsXgAAAAAAgFRj8wIAAAAAAKQamxcAAAAAACDV2LwAAAAAAACpxuYFAAAAAABItQ+u\n",
       "J9z2utRM5wAAAABJRU5ErkJggg==\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import expon\n",
    "from scipy.stats import cumfreq\n",
    "\n",
    "#The scale parameter is equal to scale = 1.0 / lambda.\n",
    "lam = .25\n",
    "mean = 1.0 / lam\n",
    "rv = expon(scale=mean)\n",
    "\n",
    "numSamples = 10000\n",
    "\n",
    "samples = rv.rvs(size=numSamples)\n",
    "\n",
    "#get values for additional wait time\n",
    "X = []\n",
    "for sample in samples:\n",
    "    if sample>mean: X.append(sample-mean) #wate time after the mean\n",
    "        \n",
    "f,axarr = pyplot.subplots(1,2)\n",
    "f.subplots_adjust(right=2.5)\n",
    "f.subplots_adjust(top=1.5)\n",
    "\n",
    "nbins = 100\n",
    "#plot the pdf\n",
    "n, bins, patches = axarr[0].hist(X, nbins, normed=1, facecolor='blue', alpha=0.75)\n",
    "axarr[0].plot([rv.pdf(i) for i in range(25)],'r', linewidth=3)\n",
    "axarr[0].set_title('PDF')\n",
    "\n",
    "#plot the cdf\n",
    "cumfreqs, lowlim, binsize, extrapoints = cumfreq(X, numbins=nbins)\n",
    "cdfDomain = [lowlim + i*binsize for i in range(len(cumfreqs))]\n",
    "cdfRange = [cumfreqs[i]/float(len(X)+1) for i in range(len(cumfreqs))]\n",
    "axarr[1].scatter(cdfDomain, cdfRange, alpha=.75)\n",
    "axarr[1].plot([rv.cdf(i) for i in range(35)], 'r', linewidth=2)\n",
    "axarr[1].set_title('CDF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Conditioning One RV on Another**\n",
    "\n",
    "Let *X* and *Y* be continuous RVs with joint PDF $f_{X,Y}\\hspace{1pt}$. For any *y* with $f_Y\\left(y\\right)>0\\hspace{1pt}$ the **conditional PDF** of *X* given $Y=y\\hspace{1pt}$ is\n",
    "\n",
    "$$f_{X\\vert Y} \\left(x \\vert y\\right) = \\frac{f_{X,Y}\\left(x,y\\right)}{f_Y\\left(y\\right)}$$\n",
    "\n",
    "This implies\n",
    "\n",
    "$$f_X\\left(x\\right) = \\int_{-\\infty}^{\\infty} f_Y\\left(y\\right)f_{X\\vert Y}\\left(x \\vert y\\right)dy$$\n",
    "\n",
    "The conditional PDF $f_{X\\vert Y}\\hspace{1pt}$ and the marginal PDF, $f_Y\\hspace{1pt}$, can be used to calculate the joint PDF. This approach is often used in modeling: rather than specify the joint PDF, it is easier to provide the PDF for *Y* and the conditional PDF from which the joint PDF is then obtained."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Conditional Expectation**\n",
    "\n",
    "The conditional expectation of *X* given *Y* is \n",
    "\n",
    "$$E\\left[X \\vert Y=y\\right] = \\int_{-\\infty}^{\\infty} x f_{X\\vert Y}\\left(x,y\\right) dx$$\n",
    "\n",
    "**Total Expectation Theorem**\n",
    "\n",
    "Let $A_1, \\ldots, A_n\\hspace{1pt}$ form a partition of the sample space, then\n",
    "\n",
    "$$E\\left[X\\right] = \\sum_{i=1}^n P\\left(A_i\\right) E\\left[X \\vert A_i\\right]$$\n",
    "\n",
    "Similarly, \n",
    "\n",
    "$$E\\left[X\\right] = \\int_{-\\infty}^{\\infty} E\\left[X \\vert Y=y\\right] f_Y\\left(y\\right) dy$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Independence**\n",
    "\n",
    "Two continuous RVs, *X* and *Y*, are **independent** if their joint PDF is equal to the product of their marginal PDFs **for all (x,y)**\n",
    "\n",
    "$$f_{X,Y}\\left(x,y\\right) = f_X\\left(x\\right)f_Y\\left(y\\right) \\quad \\forall \\left(x,y\\right)$$\n",
    "\n",
    "If *X* and *Y* are idependent, the following are true:\n",
    "\n",
    "$$F_{X,Y}\\left(x,y\\right) = F_X\\left(x\\right)F_Y\\left(y\\right) \\quad \\forall \\left(x,y\\right)$$\n",
    "\n",
    "where this condition is also sufficient for independence of *X* and *Y*.\n",
    "\n",
    "$$E\\left[XY\\right] = E\\left[X\\right]E\\left[Y\\right]$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example- Independent Normal RVs**\n",
    "\n",
    "Let *X* and *Y* be independent normal RVs with means $\\mu_x\\hspace{1pt}$ and $\\mu_y\\hspace{1pt}$ and variances $\\sigma_x^2\\hspace{1pt}$ and $\\sigma_y^2\\hspace{1pt}$ respectively. The joint PDF is given by\n",
    "\n",
    "$$f_{X,Y}\\left(x,y\\right) = f_X\\left(x\\right)f_Y\\left(y\\right) = \\frac{1}{2\\pi\\sigma_x\\sigma_y}\\exp\\left[- \\frac{\\left(x-\\mu_x\\right)^2}{2\\sigma_x^2} - \\frac{\\left(y-\\mu_y^2\\right)}{2\\sigma_y^2}\\right]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x113128850>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAOUAAAGmCAYAAACDckNgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzsvU3od8tWJvasrU4a0XyguYNrEzExuVc73svVGBO7rwpO\n",
       "TAINXmhCN4JoMlWnnUGjEHvgQK6OQgiiGLChR2psQwtqOl4MdhRDyIcQNCgmo0SvCqKevTKo9fGs\n",
       "VVX7t//vx++8pzl1zn73rz527b2r1lPPWqtq119UVfFh+DB8GN6ZcLzfD/Bh+DB8GGr4EJQfhg/D\n",
       "OxY+BOWH4cPwjoUPQflh+DC8Y+FDUH4YPgzvWPjCt1m5iLzN6j8MH4YPbLia9HiroASAf/8/+hUA\n",
       "BlARiB8H/RbB7/2v/zW+8t/5zyJ+HAcgoPIH5LB0q8/j/pvLc/pIQ/w+6N4QZLw8EzbxUf5//Cf/\n",
       "EN/0H/7nI93zbRAaZVCujWez/GyTERfU6/1AS/fA+Zm2HwT/6T/6QXz73/kHD/urC4vqODjO5Tyf\n",
       "09XLaSsHQE++TqGqOM92vQKf+/n/Av/ed/x9KjPS1c+Wvo6P8ij3qPlZl+I8zyiHnm6/AWS8lT/P\n",
       "E//n//xf4iu/9j8F6Jr+TGoN9Ws/9+nLPnjroFwGAQQsdZ7Wi4VUlri0eJ4SmJzO9UtPM8QMwEgB\n",
       "WP7GlI4NQPI3AdKeTfhZS55f2J6xl+P0uI5a60oxWYB4WxAJnHqPWs6F1etVHRFxhAmVE0AsX1Wj\n",
       "jVQBEbrfNNAAqv5uXsAR7P1Q416PRnpepv5C/nI62lihEB3nSIel+zPD88f1EeeWE3vRaAtAPX4z\n",
       "PAWUlQEkweN5JHVF6Au7EOAC1AyeFaBqOo51uhyo5wmMYnmUDmllXXBG2aOBec2U/D5zegfjFVPu\n",
       "wZP5d0BJIu+ytxWoIawo4FQdgikl3coJhjArAfrAyDgHOFUDEdGexzHYFBDgUOC0FzkU8HSKy4Ga\n",
       "7oNGjKWEfr8UxwCPZUMGmAKwkIg76h2Q3q+gPLF3VQGEBo87S3XeOiilSFSCbaSNdIHgX/ryT0V5\n",
       "Plz6GKzMakymLOQs6B2oWecOwATCo18/fn/FV//NCZDzeX6u/ky1afI6fid4emnYBUgvUPlv/I1v\n",
       "wXEDlWNUr+Wk5CPYLQgxwAlAFEkMUspZignzAN8BGWrtQYCE4K9b+3q8PDqDsb+SJzkImAACrOM5\n",
       "0V7V76HR/lm/M+YAq4BuAQjwL/9rn4pKgh0pPyq+MzC+zWV2IoL/4D/+1fjtdiGDo9htZAceQjYl\n",
       "2ZMVODLbiUcF8XHM5TI/7clqVxKw+Dp7D7cXezyu8zhAdSTo4OkNdA/TS9uiJDwC5d2gfTTvNiXY\n",
       "/rMrJrtyn+71hy0Is/vOtCfTznS1tsarfUjXkT1Z7FB7iPMk++4kO9Pyy/WTDdrsTLIrSzlOP61e\n",
       "LnOe+B9+9m+9v44eACRpJjjEEIW9kCyYquqs0kIwJnOYhOk+K6aKco29JpBPjEfqb1NZe3yyQ4FF\n",
       "vDPhAnib9MIWhREq4F8nqEoZ5Yf6xfnMlhWwUtKd5eZykZiK8sQgw85kpsx4al+IfFZJS3+7fezP\n",
       "Udo47jZKyXhBLwdgyJmzK5I9VWgIdHXXVdcorGRnG3ve6KS3D0oWWFYlmnRW4CV6VirrSsVdAuPo\n",
       "+as6QCrqBcBK+nw+jv4MaEdnwxrP9BYHqM0s3f9hWZ7l+hZvTuM1gbBoXou6u4ragbe2OQUnFDhg\n",
       "tuWo5zxM7VXgPEd7DoYZd+K4O4ZSwO1Jm00Z4GXsSwI08aH54iKRX16WiqWtyY2Ug8VIv7Itr8Pb\n",
       "tyn9X0E+kElYZc3GSkWY8/oZlAnwGUQMShJ6dLCwGt1B5artGpDbvIPvM4Mb9Axgm7E8Zw5iDEwG\n",
       "otcztfu9/i/qaFQpEowXbOnlTHY1zg4cKyNXNudIOMyuDHY6EbYlMKaTzrMyJZ+PQ4bjRwhtAUxA\n",
       "Tm9HzWxqF2/MYmMa0453VRr58uQaRLClO6SQdQLEmGGzah3hHoQnMWVjNgLpELR8ebPESjlmOM+b\n",
       "QSD1XsXGxOLa1THq8WeagTrsRweRA9LPPd1efwJkB2OUs3MA0+PtPMkLtWVp+qkvWrwTjidpinmA\n",
       "kKpgmKCl95tVRw+XIiATCIVAPmy4cY2IFKDGQO1PLQJEHYg25PfOKRcdnvgTRT1Vv6ZMtRgA1T2v\n",
       "I0lFg/lidsUaapTTVIFVShs/Cs/xvjrYxDsqhTzTWFXFlJYsiYizhFNVKbDlusXRFwf4b2CR7gsC\n",
       "vF5WkWfASXkPqoNBtwBkGbM2gOQOjvbo7d7KrTsHoT7ydY4d1VZOUrD5rFT+yubMO8y25nHk9YAP\n",
       "ogPUg2mdIcnGPKTYe0WN3MmDheFNTfYPk1QALfVqyBCwYEu3QeEy/ti2fBSewJT5sFXYq73n5QpY\n",
       "XZhBZXYAe3hgMR/Jx159nc8JyGNbfhf3V8s2cQE66LcPDp0RHZictmJJ4AYouR4KnRV72bC5dDg8\n",
       "fBUPF4hyEFNxCbRa1dlWMwCMuUkVHPByI1+knuHznEmDA7DWzyA2XM1fduByn5RHEwdyIDDnLanh\n",
       "pjQgO43Z8yI8b54SKHQwXrwD1EegmsZg7PEO8MIypa52zbS0roLzEH++VwXkCowtzdsAvZy3HckG\n",
       "v9cir7T5Im3fPwiTZ6pO0uYUSRYMR5ADUKSCDl7OhLBI4upOq2FAcEBxBmsRQ/IZRGrMYmRbetXc\n",
       "LqGal/lKGQM2XwdjR0Gqq5NtiVBfBVLv4Y1noLwTngbKbiOGMMKTN2zo6cjfu2MGdTbcDMKN6kqg\n",
       "8+ee1dimuqKqt9jFHXABSgmQ5Qogzk8QItqJgNnzW7m7oU97eB1hX0p18oTQsao6iubcPDAm7sNH\n",
       "6/nerhqeVgfZiPvLjcqPU6Hu2FkxpQjEbc0YsMi2JLZ0G1JPBw87d+xl/TpqQCaDblsmADNdbQGF\n",
       "XWxt3FTai/C8eUq40FVhh1RAueCDjp4mRSpZkO8AThJM5Zzl2aMaz92vaazXl9VNBxZpAmqXddlo\n",
       "QvuHzytASvzzgu6x805V7Y4dljdmRuiYlXDGLPl2DWubANuSDrZ2s2ijBLODeDA02ZrUX4CS+io2\n",
       "RYKSPxo51+GO1DZP6ZqAsyWDzC6zu45rxJfkUbs6kNvqpl14ztpX+GhTWiUAySzp0nhlS87xznIM\n",
       "kFU6g6eDaFZZmRm7ynps68l8xG9+dSqPeg3Qfts/3smlzKq9XwhKgK25mub3TxUNxRuLViaOAF6C\n",
       "TdUcpAoIbL6y1TJAOpbHnUigsY15njlvmfXbgwEGRqEBqtqYdVAXS88WUGr7oTGQt5fjblt6UV8c\n",
       "oBgAjIaVGKXu9M3TvK8OHIg3FjdMB5BM6VyH6+0szKHydSD29FBjUc+cRyDr0x5rQFp8o776oNRB\n",
       "iPJ8DZzWNgzEFLKaX/pZlj8vAztuOM3rKI4dEED9HACkDKWoSDIjhlCrAIe6WjoEOtVZLys4aS7S\n",
       "bczh/EGotDDmdJkSADgUckouYN/NX0qCNxeY53vwpP/Wtkw6p/QE7bCtheYtr8OTPt1K6WJALtnQ\n",
       "izsYgSjTQQf6HfFL23EGnYgUe66C7NqGrIDPs79iAmzBor2MDy6o+cCcHq3ayk2tfkMA3B7MzomB\n",
       "vgAQYMdOtSP5fqyuasunkpEj7eZ1eR1CBmYbkxYReD2+osfqi7rYxqR2hqDYmsIGsaAsyYtn8TxN\n",
       "L+v47Gs8RH5JkuUgkk6vG+G5y+xIItdsaMCKDppZc2RE1ZkHlPvMNuQa2NfxGXABWALkIdhMs2AG\n",
       "PD13lAHFPR8ZR0uPJrgAJQvTZfdgr4rufncbk9OnSpQA7qC148Q8P3kcgJ7uEFrZmJ7ez9kgDpUq\n",
       "LzR/6bbmNOhpYXwfZPz+S9tS04b0e7htOeoUTPOWD8Jr7dHzR3/0R/jMZz6Dj33sY/j4xz+OX//1\n",
       "X5/KSJOyqn5WlhxlUEB7y5YE/WaAPJiPLLsDWNmjq7cNkIewXWlfiPRvLQsgW/qReX7U7y9rfgd2\n",
       "XHfkecq7GCSm42jXeV1Hu8/0XnN6pK3qnJ5np6GMtve+OcyOr6aClLI58O7afWXOrORkoXldyl/K\n",
       "Kal4WRfqNYGDB+G1mPL7vu/78B3f8R34x//4H+Ov/uqv8Gd/9mdzofZAu5dMgCVYJzalkTCqXAJu\n",
       "ocZu5iOX1/aOJ0AWAaTO5JU6R7mG07NfJgFBnrGJR7o7LjjPfpemv9GH4YvxazTTpZwl6uxMyek7\n",
       "56Lns4Z4wuxDIJw+ng6orYHNOtjGDIY09XTkIRcKgDCwmr8ktiQ8wRcehB1tD35lW5a5IyA6bpq3\n",
       "pAUOV+GVQfnHf/zH+Gf/7J/hJ3/yJ0dFX/iF+NIv/dKpnDOg0O8VS0oWipdgcF6PYMyS62suVdWw\n",
       "HUF1rIG5Sl/OMcrMIksQdqC2M7DO5/Rs65f3Y7+kzERIqm9sK0or18HIadUTiwChon4VRfJv6SY3\n",
       "GxszFw+oTXkQiA140katMn/pN2WbUlP9THl8bFtm5tq27GtiH4VXBuXv/u7v4su+7Mvw3d/93fjt\n",
       "3/5tfOpTn8JnP/tZ/LW/9tdquf/lv/I3wb/ykU/hX/3Iv1vBSJIm0RELlpwE+wp4fp2DjMG2Auh8\n",
       "D2c7B2pnRVZDV6BjtbIDsIDW+rOMR5v4OGtJp9Mcf0FY2ZBzCZmYcgVOzj93FVr6YV7UoxWLKcaV\n",
       "jQkEAA/41IlVS6DN+UvLM/CyTRmMqFUG4hlFS1ztHi+xLf+//+d/wv/7f/9GXY54EV5554F//s//\n",
       "Ob7pm74Jn/vc5/AN3/AN+P7v/358yZd8CX7oh34oKxfBt/0nv1FBc4xdBWI3gGnXubnMcRy5g0Dk\n",
       "S+5k4HZH7FBA5Q4ub2Cz/O5dzV0IMM1JZpkZnH3+8WiAhQwhu2RMygelJUCrt7KAldL3CuSd4AJG\n",
       "NWnWGOkqJS/TiVH5zM4dpXo9bsDkek4duxGMfC1leEeBU2G7CFj81FKGdynIOmnngbbbwHmeUafa\n",
       "LgNevpdT/61tBzvehWBR5pf+m0/hCnav7Oj56Ec/io9+9KP4hm/4BgDAZz7zGfzmb/7mppsrszFL\n",
       "xuH/bVnySh0FfaIFutYZjQC5u74wZQLyODpbSgNk1ncccukY4fjSuSI6Rng75LDfh9L9tZSTyPc0\n",
       "xDO/6BBkHYdu7uOOHJ2fNc6P3nHjuCoDng+e1WnD/RCOoEXfrfozB3yWiyorMDnay1uVm7jW5dY0\n",
       "idncavL/ILyy+vqRj3wEX/EVX4Hf+Z3fwVd/9Vfjl37pl/A1X/M1c0F6kHhwflBHLoMQ/aUqi8Y5\n",
       "2LM1xGSL9k7adWAD5rEul97Huc6tHYlNPtZxYBXX3rQlP9NfzpYaxoPHZzsR0CjHtqLYeSwISJbk\n",
       "wPbjKhyHLaop1wzHzs7GHCqs2GAynnJasC72NuLvILV9/WWktnvMUwHFMSSCsRCgAfMltuWj8Fre\n",
       "1x//8R/H3/27fxd/8Rd/ga/6qq/CT/zET0xlGIDwZy5xCXHgMn11TY5KPqoZWLEY1Y4Olt3oR3lN\n",
       "hV0C6+JYseFlWX8Ff19juYijvq+w3RRtW88jby53FdIm1PCwZl2kum7KkUyTF5WAG+njvYuKS3kA\n",
       "yBNLz7B5Z873/gI07UZDW5Epe5MJlIfMa2NtFY73jRJwhzxa3bYscGlbhuPIBoVnbAfydV/3dfiN\n",
       "3/iNh+WkogkpNdRgBN71NEZnzawuBH5a2zoKFEB2VXShBtXd6Tqw5/gVIB8xZ5wpfQXGAla0dGrK\n",
       "aPObbDlkx9reoBfs5/kEshE0+nXFiJ1lIZVBV2A8Wx3hlXVwtXg8mfUXMFjzgOIUgdjyutgz9gCO\n",
       "U4Z/R/IdHcww+Uk2RHwR48zo7+JL+qL8IWZf5z6x4UGK1Qd+eove17uhM1Pq7zyC7fXvkg66VlZq\n",
       "KgOagTODu8TNsbMG36sfffIfEVdiyHQCwdKjafideYRHghTTb6V2fRyUrlnNRY503qk1wRhrRcFM\n",
       "OoTSva6ed7a6204c07PWwSbhXwcfYkgHoo6yciaqElDZvtEftni9ro3N/PDO0neXLI+xiRZtD1JU\n",
       "VRmqdJLk4155HijtbZ29Ig8ERCQAJ9aUvF64YeJYqKad8R7MR+6/+JjjrmruWDLOZVE6HZs4sIpr\n",
       "TUdNz7am34v8VRhbSvo1pKZ5flNFPRWL9ACnGDNSXmfQmPLADNDIV2qD8o45DARofQGBA1R0MX8p\n",
       "MX8pApp/JPDKaLfMN3BLm7+MuVCyGyVty9y/J+tWv9WD8JTtQPycDTuDL8oWgNVrxf7Zs94VSNeA\n",
       "82VcE8tN85MJtp7GIFwCkzqzx+O6Zus4M0qLUzMhVU4p+dH0ft2iW5jjZEr33857mErHbnQNnG5z\n",
       "Oht6HtuaXW3lM6u1ctR5zLJW9sz4yfYgYKuoVvOXSv2/WhsLkr9svwAk71IQ6q8EMFmWl3v5AO/G\n",
       "VyJhTwIBqBUzFvBE+polOd0bpqZdATXvxesyZ5Zcs+MV+EpaBy5yBM40bfkGshIHwOouvDkZhKz2\n",
       "Jqw4f9kvBDgvxXZi/oEBaaDjNFZtUxEGQAsCfDndKHuIDE/rOQMTWID1cHvRy2iwHqJdxxMckLGH\n",
       "LIDjBE5rhPpxtPevq/oSJ43+IeeNA1IqW7pq2zW83V4+CuCtrui5HZgiCBCdFWucBZLYIsC3Atrq\n",
       "eMSUspzWCIC1RQArEJbyC0Dm/F/ajiEYoOuJGYMBN2D1Zi3qKeVFsxMf9pDfDjIITaCijIOPN/Zw\n",
       "8M1c66BzcCqGQJ/ukUSCaoAHW2D6MwSwZWZTZkmhlxSMAfSUbKOZKfN6sHkQwBSw2cCe2LAtXdW3\n",
       "8g/38nnba19fEhJzBEzMzFgcO5SGCVStbE+bltN1ADcV9kE+s+pKnV0BcuuRRU13cAlM7QILUgVf\n",
       "gBbJnNHGVK60/YIlvbzSvx4UFaTszklQagFe/l0qYjIfJbQC69CcjzyAseerGqvhwsa0hNOehR0/\n",
       "CaBxQ/fdJFgzn7WVEc925H5BlOG0BVuGMyfBd8WW7wRTCr3p0pb0RiEwQLKxXIgrMHeHgR47EHfg\n",
       "LcBZVrigqLhrINN1i7yYf/T0SWV1hpyZMuPNK+vwCJDuQVnKU0ju6unMiFm30pnTnBmdOw8kk7oT\n",
       "KdVc2Tt1jgQsA3RnY/p7H2IFkXYmgNLXzpCdKSM9QPQIlLNtmXK3npOc2NIrvQhP/ci5s2QF0Ao8\n",
       "DGbQ79Fqs93p9dVOSVCtVdhHZRikS0DaOdPV1GLu6K6y6vo3Ml5c+MQMI1THT+ZVoAnmNE/fjdkz\n",
       "CA10pn2l+pqW6ewu6hC2Z7b4EaouA3Dk2gzF3sa0kcu3cBUHl28BgtrmYKa0v1nC6f5ZVoIsAcfz\n",
       "mTvbMuYtSc4v2fJBeNrfErlvSzLAcoTKl7Z6ZX1kWapvWoTQgVlBtlU1F2UdtAnGBsKWfmABzhAs\n",
       "ejdQujUkA7W2LwF5Cjvva19YZ+lif0QH6cgAqnPHt7ZIVpW4T9qUpuKq1Yn8fvIM0I6QjDieyRbY\n",
       "bG3M06cjrBpfEecLA6p82LP5GSxHOX3S/xqXSP6uwJQEYrBlpt1hy0fhaX9LpLPkypasgFqAS+by\n",
       "a5YFXbOK723HK8AWIDZATouqsbp+th3Htc27GgyZLpTM19Kxgrxm2fyXNuU+vee5giouiAw8sjHH\n",
       "9RqfWvHDegmes3RnkJKeeh7XNia3bTydOODWtiZ/fymHAdqvE8m6qL+YOcH3XNmW9lAxEFjHrNjy\n",
       "UXjqih5mxZQmH80SDJ0l1+C5c+wBxl9/RLzlMxDv25AMSqVrZnUVnm5gy86vamtXXRmA3oysztaw\n",
       "n6dcpoeKWoE5L70DuSCnXh/L3RLKA1jGmivA+vsJyMbcANPbxucs3QN7YBRij+xqHjOAs7AxGZRJ\n",
       "JoD/zRCXyZ1tGUvtrtjyQXjeH/iRvS05A1MKGPP3EMEdi3XQDdWVQYyLs1/X4r3eBkgGnU9/zOpv\n",
       "qqwH/Z6dPAvnDuXFYNXtRpnTIq8xa6TrhinFAVcvc3XVRBllGzz7m5FDVZVA8BG2Zv3Sw9N9q8nY\n",
       "RMuAMsAMYLV4IF9scup09XSse002LPm0NjZnKhKE3m8Zl7jXyrYsHzeTA2nFlo/Cc/7ADz3g0paM\n",
       "xnDA5oiEMpJlA8WHy4vj8R9wvXfcAeQhBLRD52vCq8dMOa4Z76M2f5lxaxr6rQRSRBuNQCrussM3\n",
       "TFnqoHRlIfOaxzP451li4EsPK6/uoY2ULV7AaNfGRss2MrCteNi14eg5KjC9HSMuxIjUxkDtC4Dz\n",
       "7UVQ5QveV04Ipur6oONlu23pdZY/kbdhy0fhqWtfVyw5qZtwIO5tSQbmJbCmRebzuaqtEh3cl8h1\n",
       "oE7gW06ZuA1JNqGAVFk6C4wV03WSZeb0bF9P3zDl1tbEcsqMB3TPFxh2hH4DRX11W1Mt7Qiwpiqb\n",
       "dQXMQ7X1d/C9XA0PCO8sg05RnEGpso5B4LBGOsE2I9mUHqe1sXVrSYk+Qakj20j8QUSiGYKRo5wL\n",
       "T2PLB+FJmzEjHs5Z0YHneeP9ffTJ/Aq0CsxxycrpMwP06vvGO/m7smxvFg+rvXK3GYXA2s/MngHK\n",
       "ACSptmBguvBceF8XGbvFJQxIz2c7sn/U7Glj/m0vcXVB+gCHLyIdk/25jM4dYX1KJGQ8xSbO0baW\n",
       "4H89i/stnoPiXT111TRlbDW3mTLq5cPRYyr5YM9qW/rvR+GpfzSW1VRxkDKowMBDARogUwMvAbOw\n",
       "IflbyZ5etoNc2IpZZz+0gXNWU2dAKjHvii1JXfX3g6cTU5aOZRV30f5bBt3YlG5rUl0O0uV1zTE0\n",
       "QCoxtcJnX40DHfO46aX156TvIcMOHbkBPCRLBq6M9ByRPs+pkqzoNiUgOERzEBHXjjQXJcQ1dTpk\n",
       "xFNe2Lb0vlKT48KOglRrb4Qn/YEfl0QCqRBIkaOVZGQBQGlL6BjQ10z5ogMOKqw3T5a6SocBmZ90\n",
       "URocdBswenliNZ+fDEBKMiF37TRtMjX+hfd1gUreyrSot5SeqqqzpTGExXfbfhxFZSUQos5fMlMW\n",
       "B4+nh+3Z5iaJHYHRN31aA2jxyCewUZkgjxu2ZajFYXsTIOUdYkoOOzsRjdlWZR7ZkijxCxtSBjsy\n",
       "e27XqS7ydgd7XB2QxXbsccAA40BmprQROMrO0yLRpgTeZZtvvbLuzFmkk30V6UpqbKAzywe7pqkG\n",
       "VtuSLUehg+IH7C9qGSBOUder6B0k2ldQbUxmzjqQD1YciXlvtjFBYAo5QpUnZ79L25LqWu0Tm1+K\n",
       "PDYqnztPOVKyryUbsrSoCMvDBDauF9JBewEwV0O7Ojp91bGuYz7z9AcxHsVdLa1q62oqhNNrHk+P\n",
       "WLNZI/T0+84etS/0p3QXLmM1R24yKP+LstsFG5+HyNhmUVDQfIQaO+LiKiTZmCJiHlheBUSDXotD\n",
       "0mb1/ol871/kvCeXqYM5Qk6rbekDYlVrvS9UGJAG7nwd6yOaKnkQnjtP6aAi5tqBql4j1AMzaBJw\n",
       "63vwuX83uV672tVVZr8ar3kJpFRzm9pqYDuYGRdADVsxmDLTYPn+M1n0BWy5kw0NXFk5YyktmFuz\n",
       "JQExVFu1bxppXtPV2NN+n83GzIUH/uwGUrvegRrxqHekncXJ4x5Z+86S5i3jT9QRA4ZtGTJEICxy\n",
       "NQ51recYhdKG9AFDC2i37U7hiX+fMp9nPGwa76SzWfqO+e7ZkpCpygrgRdpVfgdoTW+AnGxIT+ss\n",
       "yMzK3tWm4pb0BFcuJnjAkjsHkM6718HumzwpY8RHtmkMBbbCpbBlanG2R8+IHA5YsztPG1n8/WKX\n",
       "c7CNmRQcXth4XAOtt6ekXHka25PxKddKHjTLlUEcPT37Eq182JBC3lZrD7VBIdruXQAlMx7iTMBc\n",
       "HHU0Eio3N1JvoLymxvu5z0Wu5iPZsVMBS+y3AiY4rmlLwsGmFbxwYCYYu61Y7EoAkApGZtOp/Vdq\n",
       "qjFFSVuidw3gYI94oPypqHOMdFNAYMBzNXRcMdmYcGHOlUEBLAAHq81iaqkmcE/rK9iuBbw2tnhk\n",
       "Lf2ObemyU3cnyLZk2Qu2NM2BTa9H4YlTIg6iCjy0BgAYYHu29Hr6srid8+bywN28ZDu3Jycb0gFn\n",
       "5Q+kanpQPqurR2fK5lFl9bTalReA9La8YND4tk8pjVjSVUeVzBvEq832rOqqSDp6jqLGIu5XN1r2\n",
       "9LQxkymHEwjRzpJ+FVD/uHwB8WnW1H+Lfk7bMgE50seihg7ASgYSeeoyCZ+zRAI2gKx3vnF+5jI7\n",
       "BuIjdkyAzWVX4Kl5l/OSj1YBTccQHHbqDHAxSNc2ZC6xA6mvFZQHxeF1XoKxqrXg+A6Ajxw9Qulx\n",
       "ZwMkbeUx6jIMF9tTI8Pz+4fMsLSwMaH0l89nG9MFXJQ+5RJA3T60YWMJSgagn72+AF+ex9woyxLG\n",
       "d5dhW7IcOdgWYIWzpgtIAjbPyy4q4TlMiQ6yfFmUBmQgVRX2ji15DdzHx9GOdRm3BWnOEn0kVSqX\n",
       "6ukq7uCtC9ArCOPsA0C3LReA3NmS2S9WXuuVyZLGkwZ8n+R3A9Jtz5ildEYEwqZklhx79Yz+9vRU\n",
       "VcedfXBxG/Mw4Ri/adWPywyVsSqmlT9xXqzwCTmElL4r4MR9tgxPrQ9ckZ/AvOoTD0/ao4fBkmh0\n",
       "YKHlVwC/xJbsB9WJjIc9uVypw4fOZ5Bd6Qy5tCH7/KOW62QHwmDKlS3J9iZDyePV8tsxZ14FJBjY\n",
       "n1uvV/BudFWqBCmAwZ6CZAs68/wlx3kdK9uYZ2gXYixMdiE99xKEdj7o2ZzzO1tGHUVuVrblFVtm\n",
       "nbzYv7axLOeGe3jObnZ+oIIjWZJYD/PLS43gypbcMiADEO1M5bjM3i7VLA8GrIbdyIDk6Q9WV6tT\n",
       "Z44zA7LDh5mylJnSH3dNbhDJGHLwhSgZWGzU97nLeFqfJkm701VNJRZ1AIZ9qda3ShspwzqF1NM6\n",
       "RUJ9B69jD0qvTo5Un3u/o8SbbWkL5DVujpLvlSXYra+aVxeSnthH4Sn7vnpDdweP+AtN4MvyBWxY\n",
       "jWhdfe3wmRytAAAgAElEQVS/+3kD2vhdbQR26MxTINV+LJ7ZACQBlsBbbEdix57XgTlPjXCZln7D\n",
       "qyDi9mP2l1qfcfoBGatyHJiljJDUItGdD2h10PSGmqOHbUy70NXZuoCAKNbKw+oQOCPm/ZWjJDvH\n",
       "IdCzMls42QogWS3NQSBledQXTrBSnhw7Vlfu+UMNsglPYkpXVWl0scxoAGY+zECVRPEGjFQ/1uC7\n",
       "BuO8QGDHkLUOjQ5n1ZUB6ezY1dnJgRNsu2BKzID09Dx3W/NO4LmFfboLXgAT1fZkzyrsvZkl40Nm\n",
       "uLdTCzB9zaxAyg4FLC4BDKln/rrEwdj37ZkH9DzqovMGRiIRpucZwGbzH5JrZGMQSbl3H8tVeM7a\n",
       "V2pNCYC6Ib2zIRvQlg06sx+AWgdaOTwG6gxCbWWcJclZIzPYhEHYVdV2wPKOklbP3Subzbtw9ug9\n",
       "YKqmXQWAgFZVraoMz0Due+is7lxsyPibG3mB98+4hUSbua3pT9Vty7i/DLZV7mels6d5XcSWvN1H\n",
       "la853R+8O3nKd5XIuqsy8S6orw5C7sQAGrWenyjuYE4Qr2zJa4Atbck+0rY4s2iorUh70W3HYEJm\n",
       "uG5DOvvCO6urqJv4jiU11VpvIixAOQb0m+prKTYafbJ+JMHqd6q2pxggxFQ06kPC8JjyGO3Sbcwj\n",
       "HcK2p8+4yG1NV2/B9AYbDBh8fF70u3/U3AdotPiOAGBMHiItDlIHXj6Aq7ChQbTBbBWetiCdgege\n",
       "WAG/LLMoj2grECaLguqujffYlqwHGfegOP92FTTKV3W1g68sIFgAss5R7sEZeQWQlbvG6pw5/WHw\n",
       "Pzwzahm/B6Jrupr9GH0n853IjhSkylqoU0jdRLcxYQNPemT9bv5pV2E52IBl1Oh9NbElqJ/t95Vt\n",
       "6YXSq4qyl49/llVkAySH8Xym4vs1DtAH4XlrX0dsPfpASmPQ21ED9b13apG8340DeV6xpIOvHqTK\n",
       "FlXSy9+3IWd2PEt8tNQClIUtFyrsIv12P9ldcrhfpF/AvducivFphhAYAQRrHgsbUwiMUAKdXT/A\n",
       "qR4pD+/L7JyknIEvWbMd/OWHD04rphxNRFRrzw9w2QS8p/MwdxWe9pEzAxAc70w5NdbKgZMsuWPH\n",
       "Y9GQ/aistyrDgKJ5SGjJL1MjwZqaI+kCkGk7nhMzXgFRCHgBQEWUL+kvCGoMNFb6pNBzugN2eGxj\n",
       "SFqzpkFutbLHHnLkkY2ZNmdOjzgQeR5TNJmo2pg5SNb4auClJ28girONKmvbsqdJvFe/NlVlzXIX\n",
       "4YmfbiFapcw7AnGOlw1GXDhy7LgHtnXefsUONTK01hfAsjQDloOrTnfMy+qODr7maXVwxuxfgM/y\n",
       "OK4dlKzWvhooHYUzwLKPRPMNyMIjdZeHHODEWEJzEHvGzgTOmLA/ec4KtA6tw8MpYkTk7U+AZIA6\n",
       "0Ax88VWJpFeWQel/ll03K33E320rc1U+oTaJJATIGMvMxnwnmDJGkW5D+u9kN0BilU2pYtEguGDJ\n",
       "VYPtgDjPQ/Y0Z0MTxcaeM6NSXgcksWUuVCewFiBm2gxMVGCGp+b1Qen9hBB7ja8gUr21qX4fJZUc\n",
       "QwK4NXiogTP6c8zCj8XoRwDT1Uuoe1HzOXII4PnKJhxFpfV9chysPojmK85q6YYtleIkh1PL2UfU\n",
       "uX+PXzd+Owa8LR+FJzl66shShiLrgHjwxVGGqhCZOupdseRsH3Y7kQ9t557ntqMLTP0SZDxTB+hG\n",
       "ZZ2cOs6WVreeAboSh4OxgnK0zKvalOlP9ZQQ9LAxEx42/A+JjPt6vhdPEAZ7WlUSG8w6sSSohr1J\n",
       "rKhA7jXkYHUwG2MSCJkh+ey34G8tHx3ZHBL1TGWQ8qIhz2UOpgD+UXjSHj0GLh8BJwB28D46GMR5\n",
       "nv8a892jA7Ey3exppeVyfMDYlYB2YAPIrs4qp8FUuDOdN55PqmqqdNTRd74N2naThBwrsV+otOaM\n",
       "iWkPA8z4gNkk2PVE8JH+1vyV24Ic9j7hqQWiHfy7SV4jWwbkeDq2Lfs5wQidAXmMUaHtQrA6b4CL\n",
       "LnNa4hD61O3dYMrso2BK0CDm6UigOojLQfOTu10AtqBDGbQenAlckvOR/rlWXYzOFlZjvnAIVRAe\n",
       "HZDOggY4tHQYOzpoAaTqSuUzaCPLHUibcIg0QDOofC6g5qULxuMClRNqaqt/NaL2nceZa3YAOXHo\n",
       "QWtgTxw4bBpFrK3sixB3/mhCHBh22iAkYsrucV15YPn3g2Ni1UOm68ucJxx4qb2EPSuCd+IP/Hjn\n",
       "B1NK/g7VlJGBq0ZaMetjW/Il7BhqbahPnQ3bvGPkYc7DWUA46iWQBiBTNV0Ds4H2EpRo4LoSAtn8\n",
       "9rhQeoIOepgwpho78lyC7XqXZuPHA8dgPAKp2NTJUFlPQI7UFuCAHEw5NJRky4NUXjirP2DLkAvc\n",
       "ty19n9gqLw2YZeTP6+dtQno7z+FJTOkg7OmORaHzjiVfqpIuPK24Ps82JoETVWWdmLEwpy9Qr/l7\n",
       "1fUs52n6YwIlkOBMAR4hQevxJS4l/vGrSjxtRD84jpZHkimHuTOL/xTsqok7CnBoqq1jioSeJNKs\n",
       "f4JFnZH87pb2iCW9HmH2qvLy2NYU2gO2y3EbFByYJPPvxOKB6DNvvpsMN7/s/pqlLYlNXWW0a2f4\n",
       "b2I/QYtXQIaHFv3oamsDZFNL69mASEw64icYlLxYINnS860MnXYd5HZjXiUGwxB36swDIictpRt9\n",
       "mvOYaGcDatiUJ05mzgJUWJuO37F3LGDOnrBu6cn8KdXA9ti2dIAraKgx+UlWTFChs+elbPWyGacN\n",
       "/S7Dcz7daoAbjbsBJDaAonRsG6QBEu336uyjZBl5/SDWo99Lpiwe1rPkHZPKakDVCka8BiiTMZ0Z\n",
       "2fnzuI/8l7Z4Hmjn1ZFfRTqHj6kPewDpwHS2dHV2DHpw21FQ9pU9bf6ycjg7ekDzlta3V7blcuCv\n",
       "RwwKfFzIZsr1eA4UUL9LTAnYg/nIihkhXvZBI/kI6aLzcu9tZcdpQ+UlU7ZrATBTFoaUBkSyLxlk\n",
       "A5AzW4b6qecClGxTqklsglGKqvqAJUnYAaG4D0fRwnQAxf8ZUuZL6mzuUm3vDVsqN/7xeUnfiWe8\n",
       "Y8xZ2mDjg0zuUkCOFXuqGZjGXuYQ8hcMxsPetpxBSWwJupaAVUBLclt+i4x3snoUUq+5CE/cIb0B\n",
       "i89exiHHw1QXij6K3TmwPi+dQOWOSmeej1QbyTOeNuRZADl+sw3JYLPfS0cOAxYB0gpKIB09nj7S\n",
       "8nRBk7xvRQCzg7DblgZCTxe7ruQZcOUY/llVkE4N3/QDtoAg/LJylPlLX37nhJOL0nNwTvV10X/e\n",
       "p3fYEnPcXy/bCD2yv37hNPLyj8LzpkS8KSdmWzAcFo3mZUetm/jVtd5Qu/OaJY+WHvOQ7H11gDFj\n",
       "9jR1ldUB6IBsUx6FEc8AmhAoc+4SWIMSUe5B79BZ6XcFpot9nhHtXkFIwCY9LT/PkrAxx2RKPp8P\n",
       "enDV1h5JRNMDixwox16w89Pykxb7EA/YkoAKJJji7S/Yci1z/Rq5PYX8nCkRcZUV/OZ0xvRWr+Jt\n",
       "LdWADlmco5x38rza55hAhgpEVlUXzp6DwLiyIYMxCZyFEU9awaN9IQHbjsSeHnp8F2LawrpCxVQ3\n",
       "pogZqJnuZ3fWmKdV+BnG/GourxtpA2iH1WDvIcPGPEMlzoXqfWjwK8sjae5Zm5oY1mzZRW9nb14e\n",
       "XdjImyMxskT6u8OU4xeKmsGgIxGomF2B8wbTLo/Kjn0bjxWotmyKVl4e2ZDn2oZEZ0tiygCnqXpk\n",
       "Y4YtSepqVWlH2nY6JDrH/nFW8/glS4qTGOjPvCK+dvQpEVsgMCrZ2ZgK2diYoSG440f87qCzpXWA\n",
       "eZ4Yo+7YcjeYh1zNKmiXQx9IstVcxrXWQ+32KDzpKxGprRaj2zovV/ZELZY+iqz/iOumkTlu5xft\n",
       "WgcXAmLLYkueC0C2lTtXNqR5VBGAPBsoHYizTRmgnEAK3FJfiw1pl4hACnvK4rB0Pf0TGovbCh+b\n",
       "AhFtm4RMNqZPh9g7OrFAcchgS7cx3bbO/qjCzkfsWtdlYWdTcrzJTuxSEE3i7++DBmuBQI4QPtC5\n",
       "7U0jx4PwpH1f/eF5hNoxYL9mLpMAlfr+V+Danon5+rFKL6DrB63gCdXUQMs25GJuEpzeQdjiKIyJ\n",
       "OW5p98blKinMRxyvok/XnTKIsKT7dUAwZrMxh2f1GIsHJGcuxxUGSGvnsCVj/Pa2JSDxUZj1gW3Z\n",
       "wIhSp9VxyZbpwKkM2+NVvq/C06ZE6gjkYBKsVdRxwRrMi1ENdA2nYS6T12plSSo/1rr26Q4XjIX6\n",
       "2mzIBCarqJ0xN6DsjBk2Y3UCTXZlmbPEK9uUah8xu2eW425rjrGfWqz9scgh28woBxC2pNuOZzpw\n",
       "jVG7jTnY08Hnaqpkm4svAmhsKaa26gPbkuXDn2UlK9Ph9aWdOOVHkySYCQ6X4WmLB/JpGnI8dQE4\n",
       "LBtiY0uiNua8q4B1ItmSBXQr7yu0Xr9kRb++T3WQt9XBGWBsoDxNlVuCsjp4iqp6xZR31FdveN7+\n",
       "Q6SszuF4iH5Re/3aR2f6qbaEQMyOdDC6janMkjQgwvvBHD3qf8qgeWJJg7y0LV2GvCxf58chKN9V\n",
       "EhMWUe5oWyBe5B3ZoyeYkoEEPrv9SIe9JbPkyo7c2oJYxwtQV2XiWLGheWULg87OnaMzZAGjIlXY\n",
       "EwfNR0JnxmRQdpZ8IzZldFBKSlVVW9zZ0mklvp1JtroGp72Py4SpsAlMYCxQ13j30U9HAkMToBCQ\n",
       "rdmchbhhW0pO16zkqOeB65BmS3Z5inv2QeBxnzxtnvLVvaZ1FNoz6erQzdkba2bIvkFWfsI1q6uT\n",
       "6gpSUaf5yASjx0FxNDXWHT8JuB53gKLGgUi7rb76kA/Ap0Rcfa3x4Ci72D/Fss6wsyog8aWxLzQ4\n",
       "W5xVWGdJV8FTFfe29WvGX92yu8fesAu2BIEPTgDEdDu2ZJl7gXzuj9mL+yg8ZZ6y2pANkFg0SI/f\n",
       "OZDH0eK1TLIeX8frW8uUSGHN1XwkeViVWBErMK4P/wok1rcWL6yDr8ddZUXEBzit2W+xpF0rYp5X\n",
       "668dUyKnRNIWTRszbU3kn8a6lAx3AsEGALve2jqmSrz9DbgINVMLc9L3J9Hv+fdD6E3iXikvyjbm\n",
       "Qv5wJZMr+S1pBMwbA+UT/7x6OwN1JMLFSy8awS4v19aPnxs7OshktiWXn2xtHTpVZc0FAm364wYY\n",
       "CyhjsXkFZ6iuWzUWU5y3B1E6b4PZiGLnlU0pkmKtnh5i7ndbnS9uCQCmrjpTHjiNAUcpt5VZIwm/\n",
       "kqu0begI1my25fg0a1Ynw+6UHGtyWLqQzVV6XEAv6wV9AHwQnrR4oNmS4uxpT8/6AsiWRM1+EWsu\n",
       "83Qzqq1UUi7fAMqbXU0HMSVODLXNgTqrs92WnM4gYMac5tqmHOWQ6bgLEQwV1Rp8x5RDlR2fbmV8\n",
       "9Ol0DrjKQAfNV9ofS6ebWzEbPmSavzwR0xxqA6irrmFTajy1+FuIg7TZjd2G1MW3lFsZarItUtKw\n",
       "vT4HgUfhiRtnXdiS0wvQC49arIy0Ov0eqwagc6iiDWDsad3MR04MuVJbCzNyfMeYbjMyAGf1dZQB\n",
       "AoBtqR3blEV9va26Uj/BFCva3xUm/L6gQCVhI4spknrOGUZxajuyL9m2DKb08qI2f1nVWHHHD3J3\n",
       "gphyKKBscQehA/uCLUOuCnDZHiRwxfmOPL9LNqU/IfiM6anZ0+pF/IeT6NXoVUZJmc+homJRvnTo\n",
       "jh3ruaitrL6igjCW152zuroGZE8HwoY8K1PCWKIz5SttnuVtH4AU+5ZxANDPuVDAAer7v3L8DGAi\n",
       "fkvMZ5ZNCfj+GIwac4YKiH/WRTZlnoHKlkJ92Lyx6uOCb5mJOd/l7krGmAy6zEUb8qEpzI72B+FJ\n",
       "85T5wOPlpLxgZbxWnlhyeS34WhDzeWMRGDu4dkxJ9kvfmW5yBi1tyCuW7AC8YswzmW+l0i6YMoH5\n",
       "ok5CtGTZCb3GVYj1xBkRAbqMC6WXmwAi8dX/GaU85kzENqbPVa4O5G/hwfWCKUMelWSqxdkWDdmp\n",
       "zppbq3viWVgus0V24UnzlEJnoil/bGPJuMR+B2AXo1b5GyCbEY3/9uQ02oGPZpew7Yn6uRbi+8i2\n",
       "IMDnG0FlypzjCoDkuDk3gAXSplwwZQCzg/IlwdFTGhtNlU2mjH5TLmLbhAggx2F2o0IDeqa2nmLf\n",
       "OwvEFqybKCN36yORoX46RMw4VKg7eYIt2eGzZ0oBLyRoef0wW/Ns8uNN5E83fjsgycaMEQF5wbth\n",
       "U/rLSAUFNQoWaWJvH+mgF6aX7g1Z7hn3XtiLZV5yZsnVAY4zGzamPEhdjflG/layM+K5Z8ywFU+l\n",
       "urTkFbZ8FVBaW0aD8Z+s6sA8ASWvSKqqxJC2Jn22MRX5tchJX3kJ2BEUTOltLg7wqrVk3PvYB9Y2\n",
       "b0mAHPGFptbZUeKlmjzOtuUlW3oZTwvh3YenbTFZhj0swFReYuEM2gIuD88fdfXOoiNGTGDNku1P\n",
       "3PGZVdbF0rkByJXaOsqvVdSWfiaQY27S2HSep1ypsK/YVcqdgfyzBAzWAxCjDoVgbDd5mq15JDOq\n",
       "yzTZmGL3YM/rCVpoMAQk2Mjjmu0PsikP1dz7tbClWv9K3HeyISNtoC5edVXu4ZEq8Y4ouvxfhadt\n",
       "MclgCJ/qFpj8omuvLbBuuEgHchS7YMqdLbmd7ghgbmzHk0CozJYbZ87ZgHlW1TaW2TFTvmn1lRuT\n",
       "Fqj31TwQyb9jDoHYd5IKZ1AkM0acGJQAGbIpYhtnuY1JtqWnikT7K2TRL8jfUZbsyokpR/ywgcc1\n",
       "yglsnl7ymteW2NIHklke3Q69hcln/dkCIIY/sNpKSET1wD5kx9WIdVUWdET82pasLLmam2S70hm0\n",
       "O3X6vKQubEi3GQmoRR11YJ4LQC5A+SohqKw1XFNfEduW+0fM5JU9AT0GPykG4xcbU23bEKSt6Z9+\n",
       "DWlwOTgpPrc5hNhzsi1bn7q8dQZc2ZE725KaY8eEq7WwMJlK2Uci/SK8D/OUkbMGTnmhTAe4AXaN\n",
       "5vq9LurVWraPsJcsyQzJqik5akCs6IsG2tRHtR2vGTNAVhiSVvVMNuRrqq+CBsDReOWrEUh+puUO\n",
       "H9tzR4zt1gyJODvUogdsYYA/RMyJOgAh1v6Dkbo31tfFKjoYmS2l9rs2oDLjLexNGS9TB/cCyLUc\n",
       "O/EESxoOHoUnz1Minnb7QtMIhBidpvJ05AhGnVJU0wbAAG/+Xm6I5ediR1I9y2kQTY8sOW4SxCsb\n",
       "sqq5RVVldbakmzTbb31NUArTAAS+DCa/4qH95GhqZDxDCtukyqoB9FTgoDlMX/dqEAZogIOhxgEZ\n",
       "edYHE1tqsmWA0X4HeyLAnVMjDM7xsPk1SpWtS3lcyHGW94x7HfPEeUpMbNlfbKUaTCMS6jXZGNTw\n",
       "HbgBwF7+zpFOmrKnTgCPgFZU1wTsxITMmKeW9AmUZ6q9JZ1tycnOxMuAaZgoW4EwRZQFocaeArMt\n",
       "bcuP05bf0faueqQtGc4e87jmMwrczqwrhxKwyZTjeXJw7PYlyu8oKzQ94kxZ5OWaJadZjY18osdZ\n",
       "VgML74D6Og01kWiPKfTbc/vIA7BMXIxOxIBcdqna8NNoPuaKJVl1td91X9bdgoEVM1I625Arljzb\n",
       "GZ0p0WzLV7Qp/ZLCkq1xvcW6bcl/jdUYVMSY8jygx9AEUqVFMqc7ssBxH+DE/kIVM+VpfSTZP8UT\n",
       "6wynIU/Z36zKNqY04AaodrYlMr80F8ln/DuJfEP2RXji95R+rKc7OC9fzxuqMWw/Jhb0NJ3ypnlJ\n",
       "9tBe2JIx6hbAkYrqNiUYWCsbcsGcfDQbUrrXdQNK7ersq3SUC3ZRW9AbdvSMz1eGGguApjZEmTEp\n",
       "DmJOsiXF5i+Trc9xBgFT3NZ8cMjMoL6coQA1QJhTGsya+XRdlhPYAF0T551s6x1MPmvfV0Sj7gHZ\n",
       "Rh2Wi1U5OmoeNUoptnPieAfp+hyAI6YsKqxWkJKXtduD4XVlZjxZbWWnkKIC1e3GBsodS74EmAZI\n",
       "/63egLyIwAfMGN1g85UIMOpJjQ6Emir2KnIYqNTsUmdGByS1dywwgLGoZPurAXZvWzIzKvW/DwwE\n",
       "zpAVzXQZD30pry7ajRF3shzAvNEdT/t0awWwUsYS0jsVDvJ5sC5HV01RgTWxJam4bX5yb0tyWrcd\n",
       "XY0lQLmqxYy3Yszm4JElGNO21J36ulRdbzp8BCgbxyw7yVs4e2XsjnzQFImDLm/v9uMApDOkP6aM\n",
       "MkDMX0oMBGJaiDORgVQkwJZq7cq29H5lsBHoXFYEqaoqfW+pBFpuAZZBCTcWKlvuAElk8iA8Z54y\n",
       "HrTCKda8dvV0x4bI9P6iE0suQcwd5WpNA/EDW7IzZk57VEeQM2Nh0TOnSQKQZwcn2ZBT/JFNSW3u\n",
       "6Y9C+XsiQCiZ3absvw938FgagbMwJQPSbUtfRBDsaPOXOlCsmlMhEC/ftBfuo86SDrbS1x2Yq9dS\n",
       "FNuyH9qA1caulPE2pjEU3gVHT1A9HqgC4BeRcu0kG+2Ydg4AN1RnzDzqX1auB+hgW5KXvoXzobDV\n",
       "Yr7xnIHJZcuUBwPSmfI802YswEQBpRb1FSbkDzoHDEpSUftIaIsFVARyHOM55QAOo8PzBGjhQH4L\n",
       "KvBpHwekEggFyZS+BC9AKwKdVNa0Lac+omMsOl8DMyRsmq+s4FyxXHcCZbstCGFxtBFwGZ7gfZXS\n",
       "7xOVtwdegavICRaHNySsA8TPSoOaxvmRLQkG6mQ/pmrLNmTfJIsZtAKpsqQUNpwBqQzivqLn5LnJ\n",
       "hU15x65sQ7oWCZRcl6rmVj2O8UzHWNOKk4Bpg4AL/CA+iYXnULF3E+A4yQtLTGkqrAZoBe70UWbF\n",
       "ptGgsKXbmiCGdPB6mskMg8xBupIxlt0ml1V+dSnbQRKPe+QZ85QIlSDS+OWsUD78DEwI17U4ep4Z\n",
       "K+PaFUu2fXpodN0xp2/tEappqK8JmlRdq81YF6A3Nj1nj+sEyI36qu4AWjLlq4FSIt7OIghGtPIq\n",
       "B+QgYJ62IMBUWVdbrfBw8LgDR1G8sAIDozt/nDnFPtMim5Nty+wb/zIk0wQHlosJfICO3RUYmIpD\n",
       "ZP1n1r05F4BcroGdm/cWKp/3R2PhD57DSNiTVq6PPqu0emgtx/OToDixZDkbgKfVPKVj17bkbpFA\n",
       "WTo3qanNTjw70E5Mc5NLYHYvLAFyd172jbQyMhwd1AF6CkRsklGSLYe6ipyrjDnLVGVhm0wPD8qZ\n",
       "TAkkSIFgwdFmRDN6Qm1jZmdCLPvJ1tKKtC9HDHBmJ09s6U6dKNfHobUaG0TRWZDZUCTiIWsC4Iad\n",
       "//S1ryONXt4SmDXjWitQRhrkKLSKZ8NoyZu9tNxBwGSfaAVftyWTiRJwqbrW5XVuUzEryhKE6XXV\n",
       "YlPy2eckiTHDyUNnIMC2wqWIZRSJ0sFWDMxgDYuHOjrOeoh5WT0dSGAibchT4B5TPdRY06Diaiox\n",
       "ZXx3qRe2pf8nDkzuUwatLM4sJ25La3hed7LmTeXA9rYuzSg2ADTQjvzHVPm8T7f6aEIjTjxmYcWm\n",
       "37fRCmVqo4OP0q6mQ1Y2pQNyyZJ9LWtly90CgOn3ubAhw6Ezg1GnBQQMRo4DrsoCoPPcLzELUqUJ\n",
       "w6aWuGTk5h8PiOmPHFFzv1iv04EZA48M9daZ0sc/Tve5SWdKtburmJormGxL7h/uR23nBSDHdc6S\n",
       "DaiTnG18HSGnqaFFm1G5qc4H4bVB+d577+Hrv/7r8dGPfhQ/93M/N+XvPsWKB+VylMZgRE+jI29E\n",
       "ZQUIxkP9/Win89nBs7MlSYVtHyN3G7LOWVK8g2+nvjZQzmA0hmSnjwdFtTWpveFsGZ0i5uhJpnTH\n",
       "DzPnUm31v76lMp73OG0FnUCOYUs6IKXYk67GSmgbuUGzDPVVx0WTbRlMuZinXB6pwiJ+O3sl+Fzb\n",
       "KNMnLHMMTpJT4bpIzrPNnwTKz372s/j4xz+OP/mTP7koNb+aUGfHgxKoROZ4UXvLoa32eeTy9PJE\n",
       "u3nJCZwrW/IEKH+aBtl5XU8CXgGh1jw7V+/rxpa8AKVGeg3K7Q60hvX8bOQR98UCJzVuO8NA6n+b\n",
       "UiVU12j4sC2lMKkYK8IWjDsIB1vesy29P6F+ZhloQBvjzyLdB6WdvC1k1W/i9VriXSByWG32dzv8\n",
       "wR/8AX7hF34B3/u937scjXvoLyZTujfMmjWjHo+z6rpavQO0Dsu4j2apS9nvZq858LotyVMfs3OH\n",
       "5yWZ7ZI9i+PmXE99FO+rl6FD4zzK5qFxDAbW6XC1OI96/Xw/LXHtz+eDRB94mgfaBx859+3WP/4O\n",
       "rQTZ9qC+iP6ifuz9zU6+Ig88sIdZMw/2RY79kEwpJlcBZwPzjfBaTPkDP/AD+JEf+RF8/vOf35b5\n",
       "9X/yD+MF/vq/9bfwlR//9GKUaSqu52PPmJnfQdjAWOrU1vgLVox4fgWSwGSWNFYkIBcBowUDa9uy\n",
       "Cb5WgWehjrg7ekDAdSakQWQaHzdMmULsI7s2ZhwL1HGMj5hxDG8sjmM4rnjO8jQmzOnKIczd86qI\n",
       "36ICPc+xPM/jXtYWzMbSO7IttdiL/BXJol9bHMyI6qBr7EmytJU9aeVZXlGnR/6v/+O/x+/9b79q\n",
       "3f6YvF4ZlD//8z+PL//yL8cnP/lJ/Mqv/Mq23Dd9x98fZsghOGwi2huivqyzYzp4Qh2gw0Nh0qu1\n",
       "rhc2BlbpWg8wWLstuWRMZwZmkJVt6at0KiD3TNlU14ij2pi41/ETUNvw7t9Miv2pdBUZc48et2mR\n",
       "WN3jZyA2P3d7MUEIsi0tDQ5IzzsaG7r3NW1LUU1gXgLwwixxGxIuI0h1Ns40K7CSwwJMB+I8X/mv\n",
       "/9t/C1/xb/5NvPee4jwVn/tvf/iya14ZlJ/73Ofwsz/7s/iFX/gF/Pmf/zk+//nP47u+67vwUz/1\n",
       "U4ftTvEAACAASURBVIvSBkPJwx8YwBqEi5EoQaw1n8uVxtPSoPk0DzrLO9WBV8BKtiQSVKvvJ4uj\n",
       "pqmeOBd5BMRJdXXVT50hHZisxqn5KG6AsgX/kwSVKQV6nLF7HeTIOBBMKXQOYEIAm9QPe5LThG1J\n",
       "B7AGYOMP1Srblsf47cAsm2pdDb5VElMitbKkv752uVKwjdmZkRcVeBNGVJoWeCO8sk35wz/8w/j9\n",
       "3/99/O7v/i5+5md+Bt/2bd+2BORSr5b2wMi0Cr4GpkVdDEyrBpOa2lTWUY47rAp2Wdsa85CmshJj\n",
       "lvlGAidaGgiwyZLdEdQAeZ7Ae++FneeqbtiKnM624tLGfHToph62WbU8x2Tb8kCiPHhU7aDOz3aV\n",
       "vrZXsS2hSC+4ebxbv0U/Lu3HvUzAB29WFlbytpBtsLx6WuS1hTE3gfnG5il3k6JXKyJWagDowacX\n",
       "gjV0YUvvBAPZYhVPGv1+r9ZRTQ0KJiSQSktLINf1rl3AOmiLEHYHijZnymRXarKkpwM1bSSkrfm4\n",
       "4yCixkyKVF3NA2pL50QkbMqxIHzUL8cY1xVIxozeO8ep2ZNi57Afw57Mdqy2JbWvs6RS/7HpEat5\n",
       "ar/CX49kAjCWNXva8/nfUEld3Z3ksQKxxLts0/kqvBFQfvrTn8anP/3pZd5qhBgPby8etqTlgV6C\n",
       "XxyLxvDGnq7voyFq501TIQ2ooZrqDLhmezIIKzCbGsu2JDltBjiJKTsTMYMa0CojUXo8I8UfBAcg\n",
       "4IA0LLiTpyytg+U7s6SuYTUMYMa7yxh0fMe6bk+a2jriDjbPPwoQlVgx1FcG3tW01mR3psrrbRVL\n",
       "BwSIz78EmPbtIXkMAtEVMA3oaHnPZMrrMF6D1752dRZoLLo6OkvuRqFoX61nYklPXzp62tnVJiH1\n",
       "aWVLVjuy25Ka5+LcYXVO1zYm2Y7smeVFA0tA3gBlmY/U3A7Eva9wW9Lst8jHwoYUnW1KO+WPSKhp\n",
       "cgRgXbtIwNpKHxsxfM6yzFfqApg2T+l2XwCIWRK5YIDL2cImkrcNWxLQJvkTB+d9QAJPAuWKKeu5\n",
       "LiDgd9ux5Kquzn61DrIdIg7AbJWqpg77sW90xcy5tSVPsoMW0yFayp0VdGeu6omldSczpTNqDgJr\n",
       "lsRtUGYDae2saOzxBYicUgHrf39S7BtKOXMzZmbHc9TpUx6sxrLa6gsSZALj0d5v9E/Z+U4d1GZW\n",
       "iIOf+53PMsuHr3ttAC3NRM0C1HORXyEPLOe137vwnD+vHr87IBsY+8NLpjtLuuK/Xr/aGjnKr8pW\n",
       "NVTMiZMdr8GO4VhYOiNYZaV8dmSUiXetLNhZc1nGHDessp5ava9uR5JKFkwqmVw7J/li5Jt96Y1+\n",
       "CCA2bUFgTdvRd0n3DjMU+mIe7/9zgESNIX0d61BvQyemY7YtxfNkeGbHGtmjqrE+b6mkngrI1sx+\n",
       "h7NkaEUDhcmUzohmcxJbwklkIbMz4TSZvhGe9mcLVg/v9F7yqGywYmNJT/NC5RrRqawzJTt9AFQH\n",
       "T2FKxWoecs+SFZixMVZ4NZtXkkCXNiSrqjMgQR5SAJNaC9WKO7Ypd4TpgBVOoA5SsX13/A+3ypgG\n",
       "QZ0GUTUmBZB/5MeoJkB3BuBGeeu8Q+zPGxzxHt22rCBNe98XqIseCTp04Omy/yctDAr+vhKxRG8x\n",
       "ZSK12Zg9s/kY1GuQ7sKT1NfxCvktpafneaWfT3ZjTwPlwRoACNWUOyTzV53mRwNijKIzSxaPYFNd\n",
       "sUpnptRcpZO2YrMhGaA0zQEAbnuyw8dZMvDX1FfGJctF/mUtJ9S0JUee7TAgEiAP4LmtiSM+qRpq\n",
       "6hHAG39ottmSggAoO37ib5SQbZkrfSQZU1KlLQOq0Oqe7tzRtDERA3O3LVOFDU8tM2KTx2KWtXyW\n",
       "by/wzjBlGSGIHXu+xaYXK3UA0ZjSrl1/0DyPmLB45HUV1HYYcNvF7U0exeu525K1fAKn2pC8fK4A\n",
       "USsg055k9RUZ56V3imRMVmUt+B9anYjT2s6/EInNbQ4YWGzj1mA8wHcbkJOcQA5QnFGfnPYFSHhg\n",
       "AZwSIE51dXzQXG1LU0+DPWmwk8GQmpWOurh/wyj0/q4DdcpLBaZ/15bgdFV3JbNMFHb/Kd8HuneK\n",
       "KREj8Y7Gy/eTjRW9fB2tOtMB3iDzVIiHrsIsGHPFlE2NnZiw2JLafmc5tiELU3ZAKgGSP3g+m2Pn\n",
       "7EClcw8O3EkyWGU10JrrcaikZje6YAVLYuQdxoynAfN05lRTS22pnaur4iq8C7DblpK/CaxlQHTA\n",
       "+YAn495i7PxoWsTfdT01YoMDARQB1L08Vj+GE44ubUuxJngUnseU/k+8WGXLohKgHcyIVFdVI9yW\n",
       "vO6Yy0NzlMUiniNuqrBLW7KopDsbkoG5siGZLf06Z0XUOKuwocoChSkVqdyyW9H7oS76dJMSYutc\n",
       "h0NFAN9e4HC7kJiy2JjMlMZF5qF1xg2HjYOu2ZahxvrfZfZ0X4WjSkyZKmoC7Y48UBnxgcIGKM1z\n",
       "19xYPrGQW25fCV34Fiaf92cLYKNILhpYjDxAAW63KUtdYLCyykr39nQCq6dPnTYx4xnxiQ0drBNj\n",
       "LuJlQ+WWHkvcmi2puayNl84FU4KWva0AqcGJ2SLMlEU6UnX1BQO5cEDgNqXbmvmXmdPzKuLe2FRh\n",
       "gwULO1pnnJxeAZhnmuKItEwvXtceXzBmipZGwwRDkryUtbD2iI/kMVwlEhXN8h2Mu9BiWnjqny2I\n",
       "lAW1U9F5tJnAN4N5fzi7eVXWKJMtqeG9K0zZ1NduU3Zbs9qSZ4vTqh2aNqnM6WCsgHQVlr2vOV+Z\n",
       "0x88P+nd70AeXDlahbUPjYZMpsxOMGaE5mdY5xEM6mBLJvT5S9jc5kkbCUiouQ5EX7ZXV/XUNlXt\n",
       "g+MRaWrbsPvAqg50B6PwgN3NFtnKzHgmAma01Ex3BcSNaIp8d7nehOf+2QI0MPWRx/M7W2J+afai\n",
       "uvoKO8dC4yAFLlvBF53gaR18hREbEGMUt7OrtSeXW2wVWeYjCVQOxlMLkyYgzwAepyNYklgzQpu/\n",
       "LILFAyWv5sGQxEOGQyfUU4VgfCniwPQ/nYNYPACI0k52oRJqTo+UuUl7V2dVZ0i1weCi7ZX6Sk2t\n",
       "TaYc7xpeV0HmqRIBMJuKlfGzj1G+GECWsgiW0wWTgtILQjfhebvZlbQFOEFpdORF/sOY7OKaMuKV\n",
       "0dHLNuOf1NHu/BlpZ94XuaBgnhpxUPD0hwYg66oddubwtIeDkb72YBXWQNcXE1QVVhODEyittRws\n",
       "0bbc2gbcE4g/CBLr1DzuDHqGsA0ePrOWYEtUG9OE3sFYbUufUvEBL10vztgBSFsTyyZIMCXblgTU\n",
       "yY5sbAnJ13fVdTTgDKZJThsg0X73Vt6Fpy0eQHs4AJCOKLSXitFGswEac456WEXpt7WRktgSrSPr\n",
       "uQMt47P3tZZZphc7Mpmyf/WRuwucNc6A5MUCPN/ZwNg3ZZ69sVqlxWVOKD1WsuRHzqbRDeDZutdw\n",
       "zJw+DUKLAE6z887GlKV9TPqn9pxZcvqCRHnBwZg3Xa3eSUcOAXZqEwfqfr4yZdPbppFKl+VJ3jPv\n",
       "Kjxv7StQXqLmkcXZRpXOlgzGcX2OfEBlwQRpqjPMgKmCWp4LQDDo6suPei5HgIYdMMSSqmkHMtMR\n",
       "4Fw1jTgzaLAwQs2dp0Q6U2Kk+etbG46pOGLKIl2av2MH9GhKm944bRsQYicDIkxdLZ9incZsqsmW\n",
       "BFBVAm9r73mektLhc7QJuDHmZF/6oOxysJeV6/nKR7KZPyXq8zZmB+Wj8LQpkfpA7GhIilzbj2kz\n",
       "ZkNwY444oizZELTmFaXxqXOYKel3ApZZcuVlbWm0WGD5d0DaoZpqLH/StQekBhinT7oaY2Zw0CJM\n",
       "ua7N5jEKhQc2pj/EFpuHrMLBJ6d7dg2xhnrx92Z25DjblrGa5y5bDlW5bBNCNmTsUNDkJX6HXFRw\n",
       "AmJ9LyRfJrNgltTJNCuEY+bBSJOQuXeGKeGjYmHJtliglK8jUb6nNz6pAov5yXHNfO5Arp9njbTC\n",
       "lkqCRl+6rwHqalVnz5klp20jA2RZvu40ZyBnIE/zlKj36cHzQ4qoTB0FK1PGvCQMRAcJ1hnlY+Ms\n",
       "mYGUCwsWbNnaT3QxT+ne1tgUOjYBqn2mNhg7IAOsLgc7+WhL88I5ZTKrIIDPHtuJAYv8JjjfGaYE\n",
       "GriIETmze2P9rSYvFl8Dfnm+HwMxAVkYNgBn6Zo71fXNledjZ0Mm0NbsyexGHlS6hm3LuFdMhdD8\n",
       "Jc1b5n49GGV8kGnYXKY7a0YnqX0dAvi8pANz4G3sPpc2nanTx5HvIQqeoxQGpgGysqddc9nmvf3N\n",
       "6aN2L9uka3zW5X+zOZmz9P1CjWUpWoJOUx75HEDr8ovMq7L7GJZP+wM//kB9dHnElMFqrCbAX57V\n",
       "k96YVXWJZ1CYepJbSBZPbLM3WbVl9amrUx2ovL+Ns1dddJ7TJ7xfTmdOthsLQ0Yeg9JBRzZkBGPT\n",
       "hXEkQNqYLEEHTDUFApgyHjvqJIH3+clBoDLAwnOU6ptwddtyrabyWlehuUlnyOJ97sBztnTtpsiP\n",
       "l3U5aR7YSDMVVUnuFtd0BpzIxWVc3Na8Dk/4U3iJsKBzHkF2TJkVBACrLGV81FXtSUegUD532qSm\n",
       "KtmVHXxFRXpsV06fahEj1BU7CrYj/doAKQmmNrW2qLmKwqaAP/JCABpaY15SnQo8w+Ncx2C4sZQO\n",
       "yXK+WCDmJ3VM6oddlUwZjEhsWdVW96ym2joxZTEjNkAOR096Zf1ZXERQZIgY1F+5vz5rbXVcmzS6\n",
       "kGk0prwRnsKUEuNKe1D63d6zlkUry9cuj66iVNuxsiOXJ7ZsrAnlnepcCK7V2HmnAAZYm4tc2ZLM\n",
       "kKqoquvaWxthB8pF/2TDazau/xWt+IrfqPOAvbszNM9jetw76gxmLZ5Wti0v2q86e/gTLldPUfpq\n",
       "5VeIfhfM8lD6XijOLOiOHQdo5neBTQIgIIbc+gD1uEue5Oixk7Q42nsxWxrTMctKu05Q65vvS6Pj\n",
       "AqTXwDoXLLmI767rACXgBcNMTLpYcEBAnADJDqIYBOzdFVBQ/KJfoozHT4rbOgGNDLIxfb6Sn/84\n",
       "2nsnAOOzrDJXefNAO0+gXbAmqj3J4E0wb9pFq4wx4FImyQO7YJVJ3ldIXoSn/CXnEncNiR64s2UZ\n",
       "ccCNowlWj18dyiNTdmjifbYpy/RIO3qnV1asamyuY20CQ2opM2L+PitbrgDZQFk21ormUf9/LXuu\n",
       "SYaa6vHR7rroIwVX5gC1dhWK2wL0bj9ixZaHt+VQW2OKg8F10e7s9NHS9/YRthoY1AfnfPfV9qKd\n",
       "bYG0LeGLChby2eW7TwXeYUgPT1Jf20MVNpzLj4OGfE6GG+1aR6eJPv13V1UoLYT3ig13NiQD8IE3\n",
       "th+dJdkZxPbl2QHaWLKvCFKzLzVR2OPZNow0pdHSsnk+0skRQIJx/HbWG84fYybzpmp4RV/Cip39\n",
       "XG3dr4Nd9qHZlLzZcgy8cU2XFRI5STEceFRXWlshNfZfcGAnoP57E57KlCsgLkcVOvy6DuRUZR8x\n",
       "5Wwr8rxk+aCZ7chuU9LvW0LG7EVfiCxZUhNw80oeBqav5qG4ggCpGUe8Ila2pQiBjuKRLgAOHQBx\n",
       "sxKKRKh95+gfQBso1W1LH2wkD6H2iOmRRdvN85UGVhxzPPpryIICqd1IxtHU2Eu5iXKsPqT8rXiA\n",
       "wdd9ISz7dwjzeTsPlHgganoRf3nPW3muGJBTJtXFqmt61gic3EnR2aM8gmEYqBtGLN5TB8s4OjC3\n",
       "LMmMR6pqP9RYKdlxA0prmnl1j6W7A2PRfhEMaA5Q8d0ColV1ALfZkrnY3N9TxrPLKF+mkc4Detwd\n",
       "7FJVzUES5bfPU3bHXXz14XKhzoAgjcEFyF+7OX0of5LRhdqa3ud+g+vwtC0m1+7i9GJJpFl+OTTS\n",
       "RsgX7OUmVnSV1UBW/sSdC1Evr9W2ZMHgebIBOgIXTforpa29qAvvqc9T6uZY2pIgQHLcWmrBktGE\n",
       "NCAyS5ZzfH4l4XnN5lJabK727aRs2VIchOalXf0BIS/rW3044La2JWk2Sn2oVM63ngxAy6LPi5nT\n",
       "QagA25ILsJZrZs4pcv8oPO8rEQuyeHKpUSpMRwdZWRPrHZ/1FYeSZqMXdTTS2h6uQOlw4c6n7yb7\n",
       "HNpyTm2Zt2JJB3Nz6LQpknm6BGtQnheAtKA+il/8mae61tX7gWpwAPomWkJt1tiSgbJuo/UyO8BG\n",
       "CV/F46Aj1ZXr9XWvhVGRpkwQQWdLeyd3Ao37VmIYjbLRQ0lFTcZ0trwHSODpO6SP1wus0TDTR50s\n",
       "TeCiQvuyNBJ6J7g6wuCMa2d2nQSGwXn3aPOMAb4tSzIrku2pC3AWWxLtPrDrgOUa2B7MRNyxpen8\n",
       "CORKZcocbGDv7X/eYMGWR21DdaY99gPZlSe2MyUPtIyzPl/JfT7PW3p+LkCP3f180HegNkYssgoC\n",
       "KElb7rC3D09bZgdUEHJaIU9/8Ya28uLRGNrqsLiOf2JKRHsnoNqQLlBxtrKFIR8dfU3rDMi6Xw8B\n",
       "lYAMAmnfmaDYnQ5GXmpX8hK0l31jThy3MR2Q8DWwHryuU6n71K6r0yGFEZktz6Guzrug86C3mXvs\n",
       "/XCzX8aHzyj9H4sJnNXpfUJO1a9ZLEAnGZZFZiGcXvZGePo85S5jPU+pBYh1JPNqeIT0RKWGcZsy\n",
       "bUv2ti7nJwmQwkBVk/CStlZlCyAXc4vdlry0I5cOH2TdHah89jaxNKFRMOYpS+N73DZZlGxHr0i9\n",
       "/+I9WxvpxrY8xtm/9gkwElsOdnTgOjj99gw2ijezRJv2MxYSIAdoB6m2wZzkiQFZbEprj/xyZLFz\n",
       "wWuG5zAljyLc/wICz+I6AOBG4jknsynR6oj5x8U8FaizlqpotzknQK5/P7Ylm+d1w5LTfOSV08dB\n",
       "qYrzPbqXt5oqzS364zhDZMvyx8tuY6oAxxd4Aa6AzjQvmR9ME+BWtqWBL/8+yL7NJvt+efiDL/pH\n",
       "c5BV4cE33pyA27QuJbmCwv82iauuRUg7uWCWcdD5Dmif9OlW2Vtgr762NJ6fZPAlzrvnzFqMbUnQ\n",
       "6GedXBuWRlXv2Eeq0QqwDoppBU/agcVWvMOSqgt70q41kGXdSCEGgikj7uza1dKYg7RyptaNz59A\n",
       "85leGVUabIcAQQ4yC9sytv8QyMKO3M1bZn/MbT71GdKmpMcc76WaskFg7L/rISmTDlaWR9T28ygv\n",
       "bKma7GNUPkd9XejU3ZYUOpB6BampXGlB1abQqIcb3NNAjU5aDgrYsDjKyLxZ47o4ysheyiWDlsUD\n",
       "Eb9Wa6Eg1dif295yAdKYbycGTWmjNhTY8rtxHt9P8vNbF51uU452UajNZ2pVT1fvv3DwrJmTpjK2\n",
       "/cJ9k33pfawLRmTZGKo4nVuIhQRoohbgHBpGyC/J7k7+r8IT1Ne2uzQqGB/SPxXpLNlbsIxwrrIU\n",
       "VWh23kw2pZ+bcPTrdBVfqFBLsF6pp2Ez0t8KWQC2gNLOt0DpjbzrA4H9GXVtZavqByBU1LiXDzDE\n",
       "jGFbBgBx6cWuquscvztf2T/jilU9SgOytH7vIA1ZkjC1nS/KsdD2uG0XYn4ZnuboKdMfC9DlqJIj\n",
       "GV+fFWbDhZewN+h0f3cYEQBppI35S6B0cN+dYAIgCf1OyLI8SnzFksVpswEtp1emdLbwx2kgDRBj\n",
       "MS/JjabwD5Mj+RxtF99depOEiur95TbmxrZcAW86+FFaOzswHXhogyP3X+trhQ/aLA+tCTTfA5Kq\n",
       "64pF81rL7E4f6XJt191A51MXD0ys1x+w6elsU9Y5IVZL+0DfbcxuMyIad7Ilu4AsmHZcvxamlIdZ\n",
       "fZ3i5z6/e2iXCwjini8D5TTKtQZ0G1IF8B0E1MHly+6ocDiUJN+j2pYKOSqbCpUjbXKQ2qIfouxG\n",
       "C+lMGZ9t+dNqPt/Vah5ujuQQBrlUuexN2Amhlb3Lls9d+7pRV5nm0V54WQ9fW+K6bJwRqPejc1vy\n",
       "CqQXYGUwxdTI4pvJwqy80maqQ8v61gBdA2c8ZsQToDluNFA6KCDjubgRuX8wPI2h6h6WEteoEYPE\n",
       "4CICmo/cqKBl2mOosMOuZOeP2Fxm/UOxUx/sBlNUkEd6rO5hOZi19rJqpzVLB6tnTA6dC/m9i8qn\n",
       "/n3K4h5mdbZGKWhrDC3XZL6PdpY2hlwraiOgjcJxbqrrPE9p93vIkJrrW7vnVYnBCHAdjJ0t+7U7\n",
       "2zPsSQfkqcjHrqB0eR0qH3dQHqIYPhVIDlinls8mY2CxlT2ilQU7U5alb9N8ZG9Hpe8rV4e/S/ZL\n",
       "6SceBEjFjX4XDQ9qkdGQhS5LBDQ1IVJp8siIXLBmZ8t3TX0F6kNNBnJ9Pws5Mo6X7Q2m1BIaL14d\n",
       "Qe03j6JKNuVyVAaVR+Z7jROISMCWAFUCTYKnANOvPXExHWLHyfUjzl2d9Yhql0gNwYktHwFiSrEF\n",
       "OVrrsa9GXK2NzY8L4GC/0dLXQOVBbvwZd+/W3i/+KBynMpN2Y+9JsjCt8PK8aB5XmemjCe1sKvHv\n",
       "I81ur8HN4clrXz1h8cDTRcSoXUVo5xzhrNGsN8MnxJ04foA7ZlKJAnxoANUoNrMlCdvpjpw6pZF5\n",
       "DESWowTXxI7dodPr4rnLJShB777pJ6A6gmizAI+74Kp7WU9g2JZo74K6jC5sy5FWGHTxewJV9Mmq\n",
       "n2ofTTYlazouF9JlSNu5tw1d1M0tbkAUca0y7PEH4Xk7pAPIv1rUnl6INZtOvtXnS1ync3fyRGPT\n",
       "KD7UL7+kg9PqmwBbD+VncAEEgY1W8aTdWL8EKZ9tnYh6OrOO+rAAKTHrCpQrHO4a+BCzD0dcQ5jE\n",
       "/qKWwteu+j3cPmTPaziH3BN7VGb0ecqVquuPvLQpp9/tBe2n0CCXHz0Dk9kiK/mpTdPjQgmhDrN6\n",
       "OhHJGB7uflf5/I+cZzzWspQ2DSqic6NM5TRtV2A0/EgGDbkodqW6rekgXQz7LPyrtA7WwqKLbyof\n",
       "HFA0lZWuP1egBH2LaY/IzD61pbWf+qqb1vCC8aE/O3xooFFbdMA7CPjyuVklz2V1AcyVU+iCMVMN\n",
       "Ru0X708CqvcRT4fwYMtrYIH0RWTTkMOQm8aXBjWZu5LjrSxfhKc6euxXdfSAXuBCpa2XWKdOICMg\n",
       "Lta8Xi4KoE4uC4a6QNNoXuIkKCtnTgAnWG3Fkg5iAmRcA3PwVruT1dYOyvF4Or+DNaiIiewkQan7\n",
       "qze+whgSyW4nlrYlsyVvjqVx7Qn+s+rbKQ9uY6TjpveLq6t+vSz6gbcIqXKRZ1df8wbWNqpwvrsC\n",
       "Y/1ogtsZPhK8G+rrCKm09sH4oniO5klhk7bVWTIaEqSqaJXKOvfEI24F15L9gGVevbypnwQ4BYMn\n",
       "QRTHypYsAJ+B6ayKSMvmuAJlHIpgxrYvVsxXesGwMU3FnW3LCgj2xoaae3TAwADr3bBu23W7b/qu\n",
       "MR83gdSbVdmZmkdR/yqcqaGXAlzrqL8fo/L585RTZh4+oKxA10efGm2gi0YH5kZPcE/ZJW0jAA4C\n",
       "Hs0tzvZkwTzQBBVYCe8E5qgXWAEzWNXzeMkdvUJhnWgkY0NvCLMlxVTWsSOB2biGxFBf4wsPoWdH\n",
       "BZ+mVuLdkXmECfjzsW2Z6XvnTwPVqrsn3b2CkLWo0jR9FJO8rIOsrtkGLsF6U4d92h49mTBH14zH\n",
       "ZTTO84qd1U2RDa55zvuopfVOo/tb3mqFieevbMlk1A42GHBAgMP6vLIlTwIYATUA6/kn160pm8t3\n",
       "BGALqcccoRhTuqCnujrqlFRR7V7VtkRhPY3fDNZUNx97XVvjxOBitqI913LQ8T4GQu0NhSvmKzfy\n",
       "Q3VUeRvCxQvU815NE3yJEdnC0+Ypp7WAwDxyyAI4q1HLzwLwX3EOoG6ZchOI8bhcjuZayq6cPVfg\n",
       "TDDl9ZdMubAlCxg9Tue0KRHC6nux+tOX5tbRunJ4voyvPg6MjawOzV0JztExBZwEtrAtL5mS378C\n",
       "tYKOBjR7ZlW2JTWKjPULWt6J+3PKX8gDs2VdlK64XvvK9dY/Y7AQ64VvZR+eu3jgSo3l5GJLeiLP\n",
       "I21YsjVKfj9JHRrX8pF5MfIWYeE0ZBpdl0UciCmQMGZgtbQyZAfkxpYs5VAAXBw+Fu8EMrfYAJQc\n",
       "uWQ7VvDEDh+z6oqz2pbJtLpmSl5uCCRjojLoyKO2bu11yaAcj7f1/rZ3HzeFlLNWudP8Oc4sL2SA\n",
       "k3xucdbk/S55PvfPq6/y0MDXgcXXb2zJaTMiSdDOTh2KAiZw1nkrxmMETcBUKpb1F/kIFgSV7wxZ\n",
       "b4Uo04AY4GNgEiD7AgJe47oLbkvawnPxz7biD/wYAC9sS1VWXWfG9OfpzMngldYeoLTS/qPx5z7x\n",
       "+3E/R1EaKZoGthrcxZcQkpoacqhVDEMupf5ehnfHpqTf8Q/qS8RJ7z13qTOHNoEi/l6ENyqNzhLl\n",
       "afJY7b7KncWoRenjFTBBeUs70yoJ8BYBnJ08ZUplY0vGdQ2IeU0y02U4YTsRmACqqW2uyjYAhvrK\n",
       "tiU9z06FDTBuAJWq7HU7x3zlQiTYToWzMMx+dU1L1XXiBB99V+lkWOzGprpCMD1Dyi/t5ZMZIe93\n",
       "5Pt56iu93/bhDE1XedWVnaNdHfESXEX9oBEV2tKLquqHCcwkRGhnpWoWgCNArhhwBWZVXNqSY/tZ\n",
       "Yl5fCVR2T58tqkWXBAvKocN+PIZAijlyfEpqsi0pvgMks7Z/wsVqa3/n0c2Ldi5suRj47paTBKjL\n",
       "Tm2TC9NI1bSFVTsqVgbjJO/vik05gXAzenS1oKussjzmRg3y9KwYgflMHVcA2Tq1XEbXK8dBwOVL\n",
       "+fpZgBioCdibtiTnxdI8jpfHWwa1RhWB/ekA8ywq2ZhWL+wvaBXb0lnLVvFUQAYGFu1OzehlrNxg\n",
       "N3pCpbO9UIDXI/3wAVnJWcQdSeD0eDeB1p5+aWXWYZLdri0+CM/9yPnKttxkOPAevQyPcDFy2H18\n",
       "oQAAIABJREFULUMH2iKPhYdHXM9z9vTfMUrTtcGODhQtRMzsENWfdGsCrDMNA3P+jfoViTuKHgVB\n",
       "fprlqqzbmO64YUA229IBKabSpspbva9pV3qenUm9BLVXsDG0ArsPpKu+LV1J5XtQgB09j+SsEwJQ\n",
       "5Tn8IxfX3wlP/3QLyIevlD432uXOBL2+kk62ItKWkBCkiznOkl4QgjrKk2pI+TpVweBLoFdgOmgZ\n",
       "SN1em4G5VlkdnPRYuxCNNmwh9WkQtzFPsV3SZ+fOaAoxQK2YUuM9eTqkaCRTk1cAhY3IjMkaB/qx\n",
       "fkUfDMahdWG6ATPLr4EZzBfP8XhfOpbzrvVdheeD8pIRW7Ei4a2xSoTLaEvrgepxwZiK9tGYBYmE\n",
       "gqW+sGW9LIDIoFuppi7sDF5nJ/5dPtnKOiJ+5vlh8CV1gsF20GpjKuzviexsS6Gm0rKMLtVXz0MC\n",
       "Fwigu6zndAjW7RzNXdt6CjRwPgau2utvZIecOluwlriu6fIuTeLJf17df24p3pDZv0Fb0eOyMbZp\n",
       "j3qwCUDvQx4cmsrEc4/FIUT1xmID5K2SOahKAuRkW5ZPupDTIaqxmofjY/e7i9cu7y+xpaSv8Akb\n",
       "09e/Ots3VVaPHEzEvqAIMBLLhwo6DWjUTsjrqm3Z+2pR17Jee6USy75cg0xbvBcw0MU55fkFuLsM\n",
       "z5sSWYCqTL4uXmxWS3vlu+TdiNg7DzHvJKuyyNNK7azqqJZbBBhZ/SzxWYV1Fi3Vd1uyfOjs99Nc\n",
       "dPAe6LtMJDOv2kkkVv2E6JqNKcaA/i572xLEdqS6wqxuTVWW22Gep0QbzDyebdk32lr3feZH+27Z\n",
       "cg/OyLi4T5FVElZB/T2batfh/VuQ3kDYQXHtrJnrmZMddBr2RNNKwq5YddpQnwvKKjA9nwSnAjEv\n",
       "dcEubIpWV1Rp+QHGBkwDRGVRDZUVpwEz6kJ+E8ntc4xnGZtiIazDoc5qqG3OjjvbMtVVqXN3HVRw\n",
       "8GkCuQ1SdbH6DMyomPrFHUWrfnQZYFyybVkQPDXQOtmz6m9FF8QlmbwrNmXZOGtbqJwsPAakA+vx\n",
       "u9ZOmm6h9f686IDLVPUUKTTBcFXIppU7cIFk23I+qia2tiVZi/N5SzWVlW3JvW0pA5gh7CmFYuBU\n",
       "sDqJ2ba0lTwBMEh5B0G+a7Cnprc18nw3As1FHb1deaql90vYpKA24fPU6ZmxNnu2Fy/qyiseAfHS\n",
       "dKPwvnhfgb1autrPh04v0tv7d5QjrEfVSSWNslh3smbnqsddgHk0J3WMGbPiPoXV1Tuei2TVLx81\n",
       "AViAemb9AC5sSxrdBbadh+R9fM9Xty0JfM6UdQBKD6z6QFmaoLIgA3B4WVGfu7Tzov05Udux1X6a\n",
       "ZlLYsoatfN5JI5l9FTvzffe+bvXtizdK0DJadozZO2Zx6S7EsDuDl7BCQNa8BPUSBlaCWANcznhl\n",
       "UCAhjaTyKAT2E3XRQPmEa/Fqfi9B7FgXX4Woq65abEtmJBprUt08hRazJzj9EfLDgPpuvZ1TU7U+\n",
       "62Dj0emy7/jdtWXO8iKUx9c89Gs0Ilky4gvQ+f7MU959QGrHybDG6j3nTlp9R7kekls104jd0nTq\n",
       "9WCElcBUsNZrJmZ0aQeCPftjsy0ZYGe2DpDHUNHaxexE2gxLDVgiPi0Cc1ZIaQN/RnF1FY0pGytW\n",
       "7UCZo+l6tvup/Vb90OMXXckAdLXZtO+FANWKQm7IB3YpurvMF9Ll8z/dasi6A7aMc8/5KMbLoFY2\n",
       "whqoI6t3/GJEntRQBpzWy7gar79cWj2sKZDuPUUCCnxtqoVe3pl1RSIOSN6BoIfYTBkGTmpar8//\n",
       "QHOswIkuSNvRARlfi9gnXP78LvtpW7bmRFux0/uDX2rFlqtBtvXv9XeVI/BqMAHLkTeG33NeNHAt\n",
       "swTsm+Cc/tTL2wgLE/FhOU9YAXav73dgulBmg89DK3d8S179bpdNgNZ+zSwwRYsrclWB6dMsZQwo\n",
       "cmo/whuLsCFzvrI9qx88ZVJ2Q1B6Fp2vQ5ZJFifb1x918czLxivttXGArdq+N63fX/cX7ols/7A7\n",
       "meubvy3vI4u0G+FJiwfafq/rIjUOfrnd0qdHPUaVWafHHLn65zqL63f2i7LNmPcJ9ivxrnbOdTHr\n",
       "FpmO8jTCE+bdkaSKmI/kasujXwWFb7IW6mq3LfPdBjtmeynC2ePDHd8f49q6trW8hNmp7PSp1+V9\n",
       "RtZqX58tcjUZuvZpK0T3mdluA2wZ777S8h7pt/vlnRneOlPKneUOF3kVnDfuB4DBZ9FdBBMIe1a/\n",
       "xNVIAo6n92uNS6roEBHEv6wSF3uzCnCW7eCrz1Pjj4719cpOIxoxqozTy9CIwu9TnhN8UGJpslan\n",
       "IgYhbozSLxHJIz/dG2HLklMHX4TXE+XbbPm8PXpeau1GsAbrxshqb5428tHNS1bxAqLZrModr1VI\n",
       "ds9HgIrL/RoGLwsYq4ZcFdoYoSnkrDam8OcjFLk987Eug2K2JQns0XTlI2cvk57Z0a79fbLSOu3B\n",
       "7ZHmGn9KFdMqi+ctZRYMyPbviNNAuqmwf3/Le/WUhgyWVDzWX1d5j3HwdJvyVmF2My8uvmszZyfH\n",
       "P4vAUn3zGUOwlGSkXTwJy5oZJgeEPauyIGmtAopqEypmW3JlD66OsplzXreyJ7ud6POr/b28PSIp\n",
       "3mEzCnG01LOuexmKOfDgAmUg3g0L8POPm0J+p9hTQLkMayOxhpe0WalmceElMDf3pVG5Po+2Knu9\n",
       "mpcxK5ZHmSRwef/yCASebjtexa+OyS7tdZuzqKjN/bV3zdoGrihr7aI7oPq7P8LXo/svL5gLvwmV\n",
       "801W8L6t6AFWz6svGXQe1F2H9ctRUaeZlh5ZX1TOlMNCHT+1FLi6DWMZ/bk4Hqt3HDCL+IOQfz6A\n",
       "Pla2+OS5bc/M481uyk9B5oK1g9vZgqxHpov7C3P2ZtDVWduc3xdgPTs98uvwsAXNORYOIHqTV5Xj\n",
       "93WZ3TrcHvZefK/rRur04ck3gLmRkVJtL3eF+fIo8/xk2pgzeAvT3fl0S7J8ty2htK0HHLTJknW+\n",
       "cvHyu3dsg9Z+Dv9qIJ0e9s6rYjIXHlx3H1jLN3klYD5VfX2xF/XuG3Wv2C1ck1T05Ktr3KvYL+nC\n",
       "sa1XS1Kx00BrYAuzkgwy/fp9F7ZkYUldHHG51TfZlvXaJWtHkfKA+cytCS4BvOuPZdmrAt7+98E6\n",
       "FbnnsECfR78s+4LwXJtSFjbxpYvtLYSlN/XO/YokL/Me2UCKlu+eSQfiilHLIztwGpgJOJMsUvrS\n",
       "F8LXFnU138lt4zZU1GfysvQ+/V3vjXeLuyxfrF57VW/U8SCsRPGeJC5KtYUDLzHLnu/oWSwS2Bd7\n",
       "ATh95Lqjbu5o4+q6R46Zbkguy9X5tQJSj9CgwYI9zU+2egkVhSXVWZAP1fIq3Rad3rNgol47P3+L\n",
       "l+ijvtF8hosiU4Gl/vuyPg5z8KZ85n1eEG6i8v3zvgIPJmPvfCfJVd1o/M5EL2zTcY3a/Uq0Yeqi\n",
       "4gVDPXwuB5tdNO88gNmW1HY5H2xrUvmpnngnu6+zeXkefnm+hjB41TVj2c002MzKyAXArkBczrXv\n",
       "5sKzQ/BKRAaG5xKB7Wm5z73wdFDeVdf5dz9eVNlbCg/d9aMUVoLkIn59HULOdZ1Vzvtbb0pcMRLV\n",
       "cSnvNwa1tQeYR5RFve0xH4YXysHtsVj28vc2Re/9ZcrbYa2uvGjy91bvvuRxHkv0PeBe3ePi+gW7\n",
       "LIpcouoqn23J5aO9pOmv7v/iC1+j3AsL7+TrZYsOXh4+IKC8CPL2G2kZbt9ypW7dYKm49BHq9rfA\n",
       "uedjtULXZt4DNr8z6FyxdT7J4/tchZfQ1t1+e0XV802EDwAom2EidW3iLUC+SZYsz/T4vpclbwn0\n",
       "Pu+1mXI3j+ma5YPrX2cs1LsV3KHlFz7HI4zNe8DqYnXJ2yOC1wLl7//+7+Nbv/Vb8TVf8zX42q/9\n",
       "WvzYj/3Ym3quf3HCDdlzMtkvmn7XgyZx3nmFty/Xt27/robXWtHzRV/0RfjRH/1RfOITn8Cf/umf\n",
       "4lOf+hS+/du/HR/72Mfe1PN9IIPSv/Hriq3DLfruC8wuKFC2jNwXtCV2b/JF36J6+X74El+LKT/y\n",
       "kY/gE5/4BADgi7/4i/Gxj30Mf/iHf/hGHuyDHRq6Hqixt6YO3vVAz36JSWDRNq/50m9YfX2Nqt9I\n",
       "eGNrX3/v934Pv/Vbv4Vv/MZvLOn/9B/9oG0bKfjqr/s0PvaJb3lTt3ynw9SZG8At9+x5q0/2toIC\n",
       "/hedLboq0n4M1nzdW7+tKZGXV70Mv/Pbv4L//bd/dayIvLEe+Y2A8k//9E/xmc98Bp/97GfxxV/8\n",
       "xSXv2//OP8AhwBd8geALvuBN3O2DEfzj4JKw+jaUd2awGedpf9IPRBiTers/U7FLeyPq4VtsrDdR\n",
       "9Vd/3bfgq/7Gt+C994D33gP+u5/5wcvyr+19/cu//Et853d+J/7e3/t7+Nt/+2+/bnX/goS2Ulmu\n",
       "910of4r7fVwQ8VqBnv3h32gsm6T6HyR/zXu/pfCBsylVFd/zPd+Dj3/84/j+7//+N/VMH/gg9G/8\n",
       "upTUXDryQcZkbG//4F1f9AXQnfAvmE35WqD8tV/7Nfz0T/80fvmXfxmf/OQn8clPfhK/+Iu/+Kae\n",
       "bRs+UKrdDfYTDDVWPrColFySducVnrFW7SK86/LzWjblN3/zN+O8Y7m+VnDrzKRbx0icf5frRs/e\n",
       "3pL9Jc90p5jMtuVLqrkCtBGSPiDg7dz7I/A44V19xvMazdq1ieuCN0a1NxhyH3Wv3Bv6OatfPwAr\n",
       "eh4EvQnMNx1u33Lp3XnByvwHqLvKOvbWmsDyrxwyl4OZ3AOm0+ci4x4wbzTUi9ypNy3Y95FOPyCg\n",
       "bM0YSz5fAMY3yZa3jCK5Zppb97i4Xqj+TZlHTPfQzN0A6qU24bLoXUDfudcL2/gu3kK+dJP+lsLT\n",
       "QXmnQbT97seLKntb4Rbg1qgZKQ9YyE7T1VJO+1ri1heIffQOF4R+F5iypeJ7I9atsfRtyYHu5e/W\n",
       "LV/xud7X3eyS8VbhZbN192zLzfkloUmJ222CMHevn6WZKsUu3D2XCMZCfNsCWDD+QA/Jthzw+fsx\n",
       "1JIEPdJC+VnkaAwrDixyRIkrnjxCSLuG7vsQ/Mn6W835Si24HDlwUWkvPP8J4qsrdFNiuU7kBQB9\n",
       "vvo6qQJXxV6AGh3l9WHD+/n+aD1L2YK9pj96v6qmTgcUtgnBZpbMusSYbaWSSrCel6HnFACHTEed\n",
       "KqzXr/6wS4CmM+z0/P9/e2/zu8tylYs91QbLA0uERJEBH4ivbJ9rYyNbuSYOA25gYMBIIAQMDGKE\n",
       "lQESSEwsK38ARhYjEGKQgWGGLASSJWIsPqQLSInwvYDIFRDiSFgcDCRSboJgZDi9Mqj18axVq/p9\n",
       "9z72u3fQrp/6113V1dVdVeupZ61V1f2WeIpeAYpHhjUbZ1kyLEJU+/c20OyXx+6VTyvpieT0TmA+\n",
       "FpTS1Lt90CcA482yatGMiKe836gvjI0o+qKoRZ6Mgep0yAI6Sw5gLizE6eU5ePow5cHFtcaGnj6M\n",
       "K3MV7Jksb1cf2PVNsIZM41HTAE/DlHyOBoRrIri/6Msg+fBJljU/FJTN0sfrvPdb5LnYu1pyw2rb\n",
       "a0l6UQUTq9Bsy83sweBigU6CyUzlCLBzBtQxe7OyZUcaCbCEqIPLaaq9wcXID0j1adrgsl14tGnC\n",
       "zX7l9r8A8a1y73V83PtWzxPals/Mptw/54izTz1M9fe6XvxcKceSMzjWa/alCRdbs1/JS3qUEc8+\n",
       "pi05xtC95jt0QfvAalveClZdAyKx5tADewaP6+CxA2kF9HKK67erfz5o8jw5+ELVXIbUG9fcE/py\n",
       "nsbX80wdPesDT1F+Ekbdl50lQ1alKN3WnDTLyL194D1Y3XmT5JZUXl5UsBFcA0Y7Z03MNl/LGACB\n",
       "leM3g9+ssKaBupP5Ct5dubYb+eKkB7Tk2FWYTzejnGaTJjsH4Rvjtu/iZguySVZWcjyt+D67ecrN\n",
       "qz1fWkBS8CH6jlD7fHUFUpF7qvDzRXJT+r2PwszJHlICxy5+td26dhwItZYeOTXnrhrOrKVCCvwx\n",
       "OKHUeBkkrxrnIs9yQWS+Z3rjNc+2PEUBz9/igWoRN5W612gWdBJUA0vjjQKT7GSBW1hpAZ3dp6Z0\n",
       "A4jalp2n07bDHttYbUScbMvb28i2JJfT5U9VMdV2bbsxMhtGH5Q2qdEOwfeArvViXeT18u8Na7mJ\n",
       "QO4E3z3ZHqK+zmd+8tdZQ7WQol9GA/HPfK6SkwryJDGBGXF6WIagJAzQFEszmCNdE4eichSqZwi4\n",
       "l1kft9yer/Uyh9qUWOcrhwK12pa3QmdLRtyGDQbq8P0yni31GUsZa3twE464bicr3r1WZgOWIgKy\n",
       "GTg4k8lPlidg0YeF8z9NuN0pX3amlIvPIEam61OtSru5xoCc1Ptl9C3x3ejKwuZpZRJ9pQO6TZ5G\n",
       "SHJH+V3ItXy+F0ryMl85Iq23DW9t/fU0NhFAUdLLs1rNqpZAmIhtBcpIFaXnWSrc9Esp3bZbKqqs\n",
       "Be3DvaL8GvXhBzl6REefPVs2P19BYFQHxlJqGSEBKn/UEzCwDlBnJLkokpilEqau5o4c6mDRci2O\n",
       "YLjEEExJJNh2KBxR9xSz4WxBvd+QzI5avPCj3wrlkfxZ3W6lgSXGEW+7OnBkjX349Wu9Le+qAo90\n",
       "owJC77faRznYr/Qto0vTAJL2VEaTnx06raV1STD3rVF7iE2ZfkzmKt+NNCnbGqyxCjBHNGIeSSle\n",
       "bcrdMactQjpQb71kJBkaKIvKnaGGyu/IMreMEXpAjpi5YgdkI5ZHINBtbcnDnqE+nzWnASU/b1Xj\n",
       "E5BSGzKguL1i+qW/rrTt0o11ZMmh9/Z3+3xNJ3OXX5e/M20XHjsl0gwt3WhT1dU4P5a5i8UGWBq2\n",
       "H0WnDIySpRuBy5boIAshL14YwGI7mvMmT4WEU2cMUXt3ahb+E8Em9NoWk4EnS9qvRUl5ZDkmaKY5\n",
       "3omjgXiVZY8nZ9JufrIMJEdmPm+p0Vw76DnaLisPdKtv6vU2GA/g4ibarlfyRA2MFWAdPpk1ZZdp\n",
       "E57JPOXTfLC8gtXVkxQaFWTAPxA8dp24FrMe10sqMD0PC00+JSQsw+pjYD0GcAYw7cOoBtGWrWyh\n",
       "gAB1npJV29G9CZ3ketCgoc93DAJYboNhYPLqB7Mn8KU2ibqubV09zVzR9bmX+EVXWoZQUfX32dpr\n",
       "KlBXcC0yd4ef44loEs8ClNV23FXqwlmbmNP3+59j4Z7zYhtMLZct18eIbSCbrDVCuMDgi0vErhsG\n",
       "UIuPxHIMyEQK9uw0aKeVPdW2PPSiU9qfJxgH5kDAVXSVNsqvz1CbJTA0QlV2dXp4m7B6u2iYCYgD\n",
       "1Mx6auSLNgNf23+jJsS9WnZbH+w2yQkWE239Kb+rAnJ4psvsOs+Yf2B70MnR5715j6RTWhj9Nqok\n",
       "YJXE1K86ZaLJYhJq6VW9qgA2cAKJYYYyXjCO+DWTRUPA5ZDJgqcC9VDHkH98FYi7lKC2p+c66PmN\n",
       "uQ97tmgiH5QctGF7+nOjAR+VM4EahebpEm7mArwWg7XvNv3bFXAB6h0Qn8RefAKNNYUvOyhtFdjl\n",
       "b0wstiOwFaZy2fozn7vQLLUrfcUASw4H3cccI50jIE/mYkEdnmYeWctnHtRFZop8SVJFB4YYU0oc\n",
       "H1aEtpl5B0XmPGQjzYPtRYsfw1fwVBac6vKg9y1HwQG3CUWTOstznDzwRFwvooIz+Bd8jWbA3mBw\n",
       "ZcKwJft8t0ItK6u7KMctgzbhMYsHWkrMSRWQQhC5Lhxt+7nhrqAQEpS4bD+qGoMRRYSA2lMlgIbg\n",
       "rA6eYMgAdi3LilGwko2JY/jghqFAE6qTMd4Q2NICOWFHCszUvH4vDALk6+AsmVjwgIJR0+x9TAVq\n",
       "ZkG+T7TN4PZLhMaAiwGOdNdcVuqPumgk4um32SiL+MYP2wrQNqxi3AP70v68CA9jysWW1HMwBm3Y\n",
       "UrCpHGe4AGQOKw0xGPIhSRiPuh0gPX21DRNTAmDA2jK0yqwCyUTBgDyE2FKoSiO+NkCDmZw2sOyD\n",
       "25avg4Ox2pIBxhWYWXEozAdgZUYqgwcFH/fyAJiYumPKJqR+DfTnfqVCbmlwu1PV7EKVZzoWvvBG\n",
       "eIxNeS+FW0U6NBYA3mNH76dJOKxgXfqvjtgk6AloYPU2yvU8sCQD8PBbSzoXdmWwoQJyAMGWsww5\n",
       "xNtriMbv0TKAmNd0GzKew1h4eLwD5upxXVmQ2jAhubRTYtOrgRVxo24r4FtbYQ/GfkEKJ2hn+T7k\n",
       "+UqsnyQ8c+8rJ/eq+HC6tfUQiRAsT1JfwCdLCOcMDfFLngRWHrlbwUIexTWa18AyG1o8QB0gXKc2\n",
       "4vrVthyHACfd2FXVjRpRa6qA5KV2Bj4HR7I1CbzeLtYsRe1NzUMqrzVVHt+ojekkt3MF97ZS1AlR\n",
       "cJu1zk/mApBY7h4nz2JT7jJehGczTwlkx4/rG7Lkqwnd/NJKrMpEwvNSZFvi6v3KRUoK89mpospq\n",
       "fgdhKmIoSEnwkVXXdGwWry0msPcmG9tSzjGB6V5YoamO25LgntYRxwaexZZc1E94KzogyR61evZq\n",
       "KI9g1qzc3t3A2fRHq5ZGMOea2ZGig6Kk/hwp/xZTfmIgRXOLpmtMzrdgbcJDQXnlgW1V2gFqwOsa\n",
       "ydIxu5F05D4c5ZzvQ5DyyGzCZt7Uop6SkEy1NDt/7CzPW07GA4ZObZjMirOLbG1LOFMKzU2CbMzr\n",
       "EGAC2YkjzTX2tqQ9qB2jqL8IYFrW8rqZOdIGoixw2XyONRLO3/Wtd2UF8JodNoBjD0gOlQAWprxh\n",
       "h94THvjqVkmgfVdBtz1VC+PGqNtSrMqof6FsDGJj25cOo9F8VU3tMgYmx6f4hBPH2HKka5kRIx85\n",
       "g46BceZyoGos25Yg2xJQG/KcwwRGtjFvBgKCA4nmJ1tbcvTAzA6cYkvyNtb7eysmBh1xPbc35U/9\n",
       "Ve4VYOObWTmjyE4GLS+3S57clKePL8woa56r8DimJABuRxoFTruW3sFVR7+8VpFd4vlcdB7PG6aR\n",
       "mEZrBmhy4CTwIqUZyBiAsbdHX21J3ge7hP04yw7b0lVXGRinjlqHhCrLNuaNwKBjVpwDwMaWTAyK\n",
       "AsR1zwAeCpxW1eXBr7Yz9d+g49pXCagLaFkm4Mc8SmTbcpXNnWjK5Tn004Kb8LgpEayjB8ejke54\n",
       "avJhsF1qK3hsakLi68jTlhA4EEOtRAKmA5U7Rvve7UcfselY4xVczK4r8FZgjlQG1F7E1raUA8Cp\n",
       "FrLNU5KNeSskG9LBgwSY1pZMb5LsAcntYIDswBIqa7Rl185eBHcOg2zQQDzq4AzygsdiDhG6xuWR\n",
       "btJQ4s6eZBBWO/Je5eVhiwe2tiRITQWoUfL5UEX52mjwlCZh49XJ5RQFYB1pglIFqRUiIAvaAJUB\n",
       "YkVWT5EEPwMyronbTZCBzne25bQfB+RUB48UG/NKCqxK5RMgbjde2JKLN5WaaWXKYGKMPAjwNXkA\n",
       "iLS1/XtgS8obdVyuWzSrHKT5ugADrTOZEslcCfsd4fGvbvF+c9oqxjZlJLNKSggm0IZtORKDmuQn\n",
       "NmSQOWirMHAaYk/X+Qg+mIVNbQ2VK619dfCuTIm6aqexLUVU2M2xc4aNOdfESmoPDi6z7HkdcIZ0\n",
       "NfbS+2pgHYVZqWkr4LTNhjZY9uTS06XBj9q6grOLew0NgNxXwZYxcJvARPuEqFYVN4RRWE67sCGa\n",
       "W+FhoORRpmsEi8d5bjBCHQMQCBUEWW1ZGrEZET24AOR8sTQvg7BVUZvN7VYFpgnoypTF2aPvm9V1\n",
       "r7NqER+qruKQ6SA64DamANPuBPqZEZN1ZqaDBgTajxu2ZF2WtzKlXRv3Y0Au4OIyAMpHXakDWq0T\n",
       "9+f1e5QmXwbc7JuAjFaDc9koKtdqinHeAO5zsfZVRLxxZ0I5D2SgAkiogzVACFvLlqVQ6xCfrxwx\n",
       "MBhLOoMtIYRFWHiKEBnoEpOm9BWYDNBgyrofEyASz862ZYBzhN2oqqwcY9qYWu/FsPEqBqPN6ztb\n",
       "sYCxnrcF6sfgJltwtrJodfDcGOAaRpQlrelDZ0m2KUkuEgN2YfXAztbsgX6B4ScKz25BOijN1ACs\n",
       "jColm0cSznMjxWtTKPs8so16Gnx8JSggtkQSrABpbAHIUGm3TKkMNZlRtOy9bQlVVeVUwJxkSw5r\n",
       "0EbwDPxcVVtczq9x3bAlIy0DbPGqpjJSVzjQopxIvwQsF9J1d9uxkYFVVA4L6Fq1ljYpMr6zK58v\n",
       "m9KU0NGDrMvOYCXbsgJ2LWNQXh0txygNSzZlh6AFkMgjcnfcABAGXFVJp8o5IDofGZPodGsF1KVt\n",
       "ac4esycBtSlpb3K1a+gOlPas9lxuX+5tyTVPPHsL1oPKGGsbVK2D2/Y2OEsfbphNynlvBIqHfI3c\n",
       "hKzW1rbdaIH5+DYyH/o+paZMFiijD+vdlpbKAU+XDJCU0nkFPQNS84uCkwEDjrPKOlC6cfj//D5l\n",
       "IxzEeusxMaYD9cAQW6Ez4tMeG9sSGICxoiB+uoBnygdU81CHzwaUk9QDFAFK9ODb2ZLuFNLr6z4x\n",
       "5Mp+W9vSn3Wei16IHaxPkr682vyxxG6VC4sbCFMDSdysw2AXT83tpKKQfB5sSqA8iMSuG8Qv9XIZ\n",
       "kCGXDQMMd4rM9jRBB2LOIUA8MDx5APSvH5XZXkxpBZwZjPMLVzwg7PdQJpQACduWA8BBzlbbWG0V\n",
       "zOt9RXzTKSR72auKzGb8rZ5RAJqmUoz5joUpp9eV6nkcqe26Nt6nIQPY+nOo38AA6YN0ARnLhclL\n",
       "ahCSKanxnGcvg6t836m5Anj04gEp33+tKiqQGgLIlVsqbmBbDQkaAbmDQGypj+BsEZ1p7JE7fgNS\n",
       "f64K0JlFDr2JjFhCd1R25Lhom43WtpQD/iGs0fV812BfAlBGUwQwknp6aL1atjwIkFqn5n7WAAAg\n",
       "AElEQVQQvyhdgejdSu2/Pa6V0Sp7tzFLdnLRyc9IzRky1aSxDJd4yLKx5H3QfNzigVK7TlUVTpCm\n",
       "gmPNy2qHN/qw0VPLMeQMHybztgBP85DQJCGo6SZsJwnoeWC+hiUBeDsnaBYOBKDDljTAjKS6Wt2q\n",
       "TTm/NtCEkVoXKReBcj4fEiADMEis2duS1IQO8rWsAPOBBOxm0ItBAFH40k/5AZgpU31ZLnhf5Kdn\n",
       "vpR5kWE/V66t34d9btRXDlIesOrftNMw6LS4Cuv52LNoo6EKfS6jjKYEgDTtsXQyECBEnNfkbtmc\n",
       "M8FJYORzCZCd99WAS7YltYXYlMeAgxFQJh2DGJQbe9i4lpHLoKM4gy0BktVZtiUZgAQm96Y2oEvM\n",
       "mQY4ZVZ6xtwvlM79soC2nmdZyMB1xvS2K+eMCdP18POt+lrBeKcO+9gPZ0mkMdXtNa2p6i71Mfbz\n",
       "8+TkIdCkRh9TFfS9qqm++mbpVLham0bartOPA+M8dY5wFTxfYqfn94vWhw8WBoT58asRTE9gBJA8\n",
       "rUIfZ66NNr//amowN7He15uOmI+Zkbfl9a3KgBWcKwBbVjw26TswIuYbkyOH+tNlY8D3Vc6ys4dl\n",
       "KQDpQpSalhsS+RzLd1Vvb4Rn5uhJUXrodLyUM8DLUzoVwyu+tFcZKeuAp8BZRttl1G1G+zEg6syZ\n",
       "b2mcPhWCszIoJoMCLTBDgMm2dBCqUGiD2svMIlZ7Etw6ktnbJCOuAz1DaiYDns9XYmVJe9bjBuCA\n",
       "5jwSCMdxYBz2RnVWads+KANo+gRL7U/On+SgApNU1O35EoqJdUt+nxum5MDq6mJnApk1eYSRABqP\n",
       "ZmhYdF2BUVjQmSTYMnVyIwxp2gRo8lHxJtR0PhxLFDcHUGGX+aLyPBe2pIX5/M6cuvn0CDfGKHGa\n",
       "x2RmxLA24GZgOzDHMzgRjLphyrAl0Z6v7bcd+HZ9VIFrICW2c/XV06O8dbVO1dw4P8kiyzLJLIea\n",
       "905MPkB9hcpHoXOufGqI9DpI8yKXsaU3igq663DgwdDzxEgYnWCADNBhBWMDWme1DqSN4HT2JMZ0\n",
       "BKWFBRJAtXlMr48KrP9GCDl4BqBxibqbnuZxLYpBqc/OUWbJ5I3dqLE4jhKP/Sz7yKxXWXDZ8rOk\n",
       "9AKqtM659l/payA0qQTYLChx7c21r5wfMJt9L9ea7blQX3Xy26OgCjXDh6mfS6Us3UnCGp7VWRr5\n",
       "JIAg3NBDhZ3OjdTBaIWH3/TYAe1qkTo7POY8ZAahq8HKlMPBya2jnCYjfe5j6DuWl/qW5b0HlArE\n",
       "+u0elC08w3vbcz2HbRstgMUav1oUkBcHNNfRYIsx0nuUeTF6tDd7Y/mrdWnr1NWi1t7LksCjmLIZ\n",
       "JeqHs4S2CSDx63k/IwNsWxKx5pEWAI+SM+QRNA2spSOXLeU5gPHqTaFiIVjzNWypgweOQxcA8CPo\n",
       "M7D6CvjKn+SJrnFXXVFsygrSAOGivpbN5iUZsNcsiah/A+IeqPzhn+i/3C/cN9FWWfXMctCCcIMc\n",
       "oXZMWR10I8tvAe+TsCTwsG/0mBpaR6J+FHGmtErbnmTR2LIf6XTUNLYhNdXKCUyTKjuaju4ExTtf\n",
       "v3a1Y0u1GydoDn2/UWKUdxW1AFpB19qUtjcgAhi++KA0LH954Jj5na08PYPSbT4HZWbO6vDZbsfR\n",
       "sOShTp0egKPs6+C23bjPWA6sKVws+PzsQ2NLbOQpaWko8ohIS/cDtgC858saD1Bf8z6pprJ/eFYh\n",
       "POrgFG1M8SzhCAo3+QTkPI69qqtbsF0IwjIqN2As0yLznM5V2DkGa2FLE7A5hUErAnyA0D01z/G6\n",
       "mW0Z8Y84tLlLV6MtfXAaATCBBBvgjQBeZcw6yPC+sTP3gAMd1/O5H+p5U20ZiCwPUpZdsnyG9hbX\n",
       "xNxlXLcDJMt3AukdbPkwR097wg754XlT4HkFxyp3sjQ4YOtE2WOLMRJwB9kTyabkztXRtLr4V/VK\n",
       "MMa5AN2nO8zTSoDcsWVcCz8fYfh+aJsNre/8wR9lSxu8eIXPAEbtCb9drqezKTl7FnvykikbluQV\n",
       "QGmlEIM11HpXW30gyu3O61x9PxqPuw/AJAdgNTbaNY6zNzY5cRLQVufOPaC7FR7DlDaoNKNFtS1d\n",
       "oKSkjQxW+0gUIGQ+aUPSCOqTyRKNPQACEFYWWoB5zzZVWZ/WOMOrm1mUWLNhS3ugoaO0Lyqvz2jB\n",
       "1FJSq1qbYBPi63UrMCMeedi5g8KOILCtgDva86tNeWBt26YfLvsl+rF+qylNb9TB3BkUdH4lC5bh\n",
       "fq1r0QA57x3hwWtf51NJqXzSzzf7VPmxyaNlLzalNcoIj9vwa/P0SNvZGwG49Lgew5fZjZKOwowr\n",
       "WxaAe7DjcAJNNTf2riKcY36N4EaY7AUwO1e1FcRwvT3J0yIbljwib2LF3aKDZsuLBMoxM6Ma4lWb\n",
       "4m/zVJDWNa98bRGwxJqdDDIIo0zxtFvhGa59DXSliqTMBEZiB18DC4nGZg+ZyqWruwRG70BmznFA\n",
       "1GFzNV8pJlQQsIPnHpC25zq2VJA4S9oIZKP/4Y1w/QlJnc+UpIpQsKYAgxHRBhZntbMDpwPu2NuS\n",
       "FYh3bsPUWJA6iwac1sfUxsn2ozR33rgKSvKng5pPqSUQUnmNJuLApHI9wdKfl7dE7L3A6tSZD68q\n",
       "aG0gVJVh8lqnldV82RDXxrUoAJEDgmz/+VQE25ZAK0ix0MBsSZmAPgamhzXALZo2JL9LieOIUUOF\n",
       "N0B4QM6zsGuw+vQaD0DOidWGLZ01uYFqMBbkY2ZGi9viAFJz22kMBuaWJZkhA8Tz+PC0AGQeGCtr\n",
       "rvOTyH3IeXw+CA48UJ8zYJcmK2teaz6X3UKzMeuQ5f5WePzaV9iIkUeczuXsLIqmkcimdCah+7Gj\n",
       "JzW8s2px9JAg8uiaRlvkKZDKeJPlJuBEpz/szY01b7EtnVFOBy17B/2/qaWn5t0Fw5uMdoRevbAb\n",
       "UBJL4kDv8Dnyi82VJQOcMR3i9T2ata6bKROfaE0MaP0FBeGR+taBN8LBY4vGqroZAmS7HUizjLKW\n",
       "t/hCcD9DWnio97WbAqkVWepKDeCeLwJcP7eUR9CFPYcOCJZnDPfGjmqjVFWJ2fJqY5vSWNQqwOAs\n",
       "bAmMiTW7zpfu0K/2eBtamRuWxBr3MIYrBClewJVf1crgYkC2XlnytPI2+KXnZrtPxT1yH3k/I02F\n",
       "WJxZMamoF/KjF4dsCoI8ipwyuJMtyWncdRfhId5XmueOtAagdm5uOpwV1VXUTppOGy3AsloYVJZ3\n",
       "WIx8sOOBtOSuA2BdIOAMlxYNhE26FSBaNLBlS/W+imAyCIAwHEdUyfAJBR0T5qC2E46XQCRjkXlI\n",
       "ABwdIEcCZACNAFhtyR3zXbZXHAtPkaDJv0mr3+TpPLCr3EU8zTeS7CQhU8dFCzjS/tJ9boSHz1Mu\n",
       "D58qXjapbaVAHAHYANuOKeNa6zz/hg95adv5yosRXMaBsQAzwGo2pS2fYyGzrxEktrTpEDmA44zn\n",
       "XT5TRw1L7ZdY0jA5KN4FAqLHGWQtKI+GLWf9ly8TsC15HLktaZFBbpucb2tL1o0Ax30/tSmrIw/K\n",
       "N7QsAq7YQFnnJZkRi3wv2t89FKnhoT+vXvXtWqGkIniLSlziKmu5did4PiWSbQrrvDHMAWDgQhmt\n",
       "FRy3RuVllG88s0eor2IgZLY0wRX6kcrjwGi+G5nY8ix1H1R3X12wD61tuQCqB2QCWo2TLWmDVLw3\n",
       "eYsd72TDi+tE0xNYiUGT92+Rm9gtqioJn4HV5bUAb3H83AnMB6mvsfY1jST0sE2dlrw+1cFxdBt7\n",
       "0kqnCJr5yvDQDTBL5c4XXbmzY8uOWc2mZLacAAXstyb9VZDzDLBi6C8zh62Hg1+cPKnBSsOAWPNG\n",
       "yKBk1RXEksfKfKMw4pGBF6Bdgbis6Lkc4Lj9ixpbtmoPLvOT2vduUy6ygnKMmZdIBHR+AaFtTior\n",
       "c97j9HmA+ir+XqBzXlm25MkSlaACXKfnkZ/jsxzuEC1h8H2Gj5zLfGVRjSqwKjhv25hcTrYnh779\n",
       "AXPieC/atQfNRZ76XFAgpxXmAeKkdlA7JVtSSKNgarSkoU0WwBl23zofOQKcDsLRsCbZmVZO5OG5\n",
       "y8p2h4LwmjU7NbZjVu5zXhoXwqPyIyPL304WC4MwENdpP0u760ceATxwmd18LvueDghsGyACqfGm\n",
       "cyeKtFHPPlfJ3/LhEQ8O1JDZWV7MV7JNmQBYbExnvqQmlekMPR7HXIfqn45UD+z85s4RFTlkMqWN\n",
       "pDjncyQV107PcgGdo4wTWukJUB+7uFFlKNMzUK094IOPsbKBsk57LAxpzHcQQI1ZbcrDva15qR1a\n",
       "dfbwds0sWYDYmRWLTWnmCbcha08rM2Y2zCBdz28Yk8mFGHPK/+3wsJ9X931lQ6b5WhnBMgL5uSKP\n",
       "+X4qnEVFiU5DsSumKmqbuTRdtWvVqgtvK81b1s2YkhcX1PlK4cUFxzQc8zdeZ5pgLkyYlR7r6FaI\n",
       "EgJUG9KzsmZwUHw3v8iMx4Clyf/4ekGZBqlAfFrvrIPvyP3HKi0x5bpIwAbr3CAZoAjGrPIoca5j\n",
       "Sj4Xsnsblg9y9Eh4r6imrkqsqEqNIlHMPDfo2JbbsZoCWRq886w5S44RK2Ws4w1UPk8ok8UatqxM\n",
       "ugWirdwhYFYPrGB+Gc9X/QCI+cjTNFoH6xygtEFOA2aRDHgVCJRZENmWnHWBP3ty+Jj6WmxJMHBt\n",
       "cUEFZGHJtf2u1djZb+v8ZGZLhCwYcF0ORisXi3yY1pG0uaxxVaZMLZ7kV2VH1ny78LgvpKcHstUq\n",
       "89hoL02B+MijqmuyBQImpk6YalCBmTuHGVM7ZIxQhUc4ZIZ2LANtFBV12oqS044JHlZhZyOUucoE\n",
       "5AOD7EgHvQEPWiQG4qPME7imIvv8h6CsidW2GfA3TiYmR8pSV/LYsdmNkz0rIDNDsn25deKkuU1z\n",
       "3BwNSDuv6pFsR1NN29e3fJBG0/dmP5rc5TjLR54asbxwgknqLY+HNmvQaXk3wmN/Xr2h+HkumI0f\n",
       "WlDqwOqAjvZTHmUBW1qVQZ3jo6UB1Za4sbrprDkXBXQ2ZMuWNi9JAKweWPfE2k8X2DnMa22+0uPD\n",
       "5i0xl9ZBJvDtK8w+qtOI5nWYjZZsTG0Sd2BZVRWMUScoKIvq2qzkqdMn6RWtDUsuHtkxWjVWyn5J\n",
       "Z9Z05owBN+Vp1NbeYwsijSy/V7JJLb5g77liSg9VqwLQroEFAZfZEuvLzg7OuhY23TbYzz+mxZ1B\n",
       "6aKAyqCb7CgsPHdvxpy6mUpKYE2M6Q4gofgJyJyqESDemwRgi92zikEAtQYdtAf0foiEFpRlsCFG\n",
       "dFZLX7LL61jbtax3seE+PVjyWPLIOKI/d7akv3XDA3aWldn8YVYlzQ0kj0k+0xgYslwEvnptd+Eh\n",
       "b4kEU1kaUbrkCgPUEKmgWjDJ38jX5G2kPfy4jLIMXBgIpkc2eWZxTF4n1XVd3TPCWTNCIIcI5DhU\n",
       "y5T5uQ+qns+RykFxmwohG9KW0Z28BG/WUvRpQ+aaYR4FlLBmYDDBbcjBtqa/3UFzkTz9QW98cF53\n",
       "BjULDvareNSmnCvhEWyXGbCaKcaYrYNv0aZWmVmbbQUwmmsycCmtMOyt8CCbUgAafSy9AtLPN6NQ\n",
       "HaUSIMVsVP4JAwORNGyoIOQOGqHK+iL1xJjNyA22M1W1HBLsqN5Vty0NqD5HaZpCAHkIVD2NwWH+\n",
       "WNCJMWxAAHzpnTaS6K3DC6btDHNiWSua4BZRGwQ8ZnBb4wqEukqAzO9Tki1paizPT7oqW5juUADy\n",
       "e5PmRb1o+8ye2p8jwAYGq8DZUlQ7C3mq9mXOm+QuyWKR1SLHCzjt4EZ4gPrKH7ky9QDt3mk/DlN6\n",
       "MALJ8x1MyUztKgqNtK7SGDARHWyOmG5xQD9fOVzwxJBC8XEoCwogx+ypodOU9nskA54wgcpL7Xyh\n",
       "PjMnaJSKAZDJMrFoQeQkzdXzas9tC+VnOgFyGECZEc3ePIIFea6yLsU7diyZARcLBI6cl5mQmTKB\n",
       "lfpda7zzpPogXcEULZWEM13HxNLsy6Xb8BCmnAcWCWB2I8miqzcjDzMlXA1bbUr3wgqDEMSkceyv\n",
       "b1HnD/aE1pU7aRTfrfIpcVZplS1jcYGprICt+Bm6aseAafOSE1rBlGmRgrGmix+1v0LSBDVCMxVC\n",
       "TOlvrHCcActqrTFjZcmkupb0diok2C9sSPK2OjMeJc525KavffDP7bCos85u1/LYIXuRb9BHzW6E\n",
       "x/3qFuwheTok8qSKYh2BPC+ooZgcmvlK7pS7NgWmj74lPje2KTMQ5dDpCfa82npVCWDa0JFszPNM\n",
       "bDqreCprKiBxBvAMqPbFusFqQ+LJaGRjygWUQHL0AOHcSSt5sLBix4LVhjQnkANT1dVsSx6zrRqA\n",
       "Jo2GNmbKFZDEoPdurnHAtQ03uzp5LTLKcZbYpOYuLb+Gx315YKH2LDhpLpJGG0iUkViUBGsma3nC\n",
       "dqV9w8dy7kbRrAKlF59ZJU3CUkd2BWlapaMPq17YgcPxMn+V2Zw/kxUTMFWABac6hGgFjwz9ZS9d\n",
       "dmdsacDEiJHLG2kOBcsyO1VlHdgDAdy03hWUFiCMuUvaL4AONTYxodmS48jHo+RbVNjCjLZdADTO\n",
       "ab/7PGPYk0hyQfHCfq08epqEzJd97ZJdeOjvU0bFApDZ7p0CxyyfgAxQY/GnJbVx+bOTDjTLzwpd\n",
       "gBDUeQNDC1QQqApbbZSwKenXmo8DkPzrzdm2PFwTm89H3lgEKya701b2nOpI8lfJxJ8xhueotzt2\n",
       "ioahymvmUFcR4WdNhTXW85eXAfjCALcXG0Dy0jtTcY8MuNWWJCaleD9POZ1CsaTOnEQFsF7TkIVO\n",
       "gwKnd/OTpNZWmU2gBQkqBRFJ8n8rPIgp8+hRAVntxSUNKKBeVYdJkisweWHC4oFdVJgJKtF5SV8I\n",
       "oCppTINMVlzszUOnLyqD2vyjVWwcmSkd4FmFFWDatfyisw9oAWKYTemwg7NnbvE1OPtzPtYMDFCW\n",
       "97gAoqmuY2XKsDEbxrStpAcgA9A8H7ky5bFRS2NvtYwBOgPSGY9ka8+KhRHpfJb3eRdh1e8iPGzx\n",
       "QBpdUmWyjdkyYwNE01aVXDMwIY1HNquuAAKgrO5I7mgomw4MZFXWVFaBv33htpHalrryZs4ISQge\n",
       "lOlEyMZUkEEwhFTZExgHf59H4vqkUwk11p2dMhRoob8qPjMozfs6QVgAaW1xrExZbcjUdpRebcm8\n",
       "QKAwYFJhbRF6MT1IXe19C+ug7jLozcjqbgNSRDNX/034TqQH743wsE9MzuPKhJIbowDXau6NSo4M\n",
       "M8zzfCVgL1TnaRjqtMKWbouICvlQFdZUU2VJm95gtkzfimVmNNvyVFtM7clZTYHZnJMVERpYYsPJ\n",
       "utPWxLQddTmPnDLnPscJ+8UtXwOr9mTEbwR//hqPKRADYzrHYGNPK6mpowDTwZpsSQZfBmYFp9hC\n",
       "At3XgTO0He5Xkx0adPUFALcpE1Na3gDrlEUzq6x9L2QWkb6cvyM8+AvpEc/7Ak744aIqVKYU2our\n",
       "sAbIzJQWB8UNEab22lK7CcLTO90YpWdLW9UjG9vSHCUy1VRfuwqdo5T55Tte9WOLBg6yNQ18bkse\n",
       "fQMNbqgbYUTd5jPmVT2xGCC/T7l4YJPHlRYIFLW2OnKEyq+qqp1PCwQIrEK2pfkH5khitmbt99HI\n",
       "gTUhOXUQTQnOJzldyjm/jhgSdK4e78KD1FcFSHrQEfHaEGUkisYYDmCveAGmqbRzQJsR3wuNoEBR\n",
       "aVY2HRJsKfRlqpgOsa/Y2cew2IasqDAgWj6oBqrxA/7mR4QTw4Cpo/a0Hed1tu415ifFG2H5abxN\n",
       "SDblwpI0ADm4kOL1I8rOfNW5U9m0HhdbcseS0oA1mR/FlnRZU83K+j36P8tfJ4d5lQ/aja9P8qyC\n",
       "LN4ft/vkYYsHFptSkSOkigKFHVG2JU1VCf8GUKTHq15qY3Z2o4O0AJTOGTv6NIF2cHhed7blUPaE\n",
       "ng/ADmhnGQNBIGdeQGB1wRCMc+Yfp9bSFiGc5pAqy+wQQL0ZDGgNUw6718KQwWyhkrK6SjYksyYB\n",
       "z5nuwpZcpjosHzt6OkB2AGWnjwMt+tPlxwHJMpRZ0qHVANLzaAKzaMXBLhy3s+zDZz7zGbzjHe/A\n",
       "29/+dnz84x9v81Rjl0cTfz6hh68VZdYESqNaGdG4IDACDDZqyNpJpRMNiMmxUNNcSPI7fmgFq1Hd\n",
       "in21vJnPk+7NMa+ssXnAmL7QNamvO25vnN/mE3nag96TRNl3gIx0Zspcd3POrECtLEn2YumHlHcB\n",
       "I7Gj9WkCVNGWdDDLDqIibx1LguQUDEgX6yTb1YzbhadmyldffRU//uM/jt/+7d/Gm9/8ZnzzN38z\n",
       "vvd7vxfvfOc7U76sa5cKGUvyw9txrXhXBlc4TNIEzNwJ1om5Y3wURnTwcLY11dRalKZCUNmSbEtP\n",
       "O5RFLd1ABPXIHtNLy0wpwfzGdtOWFNg7lHIeGEes8LHGE4xw+DxJMGZklZWZ0YBSmPJqXWvYkgy6\n",
       "6ti5siVDnYXp+3YeYUfGGlfuxzL4OkuuG0gGXVZ3MltkO5lZRd7hpsaDQPnZz34Wb3vb2/CWt7wF\n",
       "APChD30In/rUpxZQ6iOmSsTIlCvkgjVy5ZbKm01p5wflG3VEFFDRenyh3tBmXx9wVdYApWtiIeHs\n",
       "Ydsyqa0H0p1zmxy0B+DTIKcD1BpinHEPKEBtSlSokVw1fsLgK30YkAPhzFFhZ+dOsjU7G3OxIcu5\n",
       "pMYOAqJuiRWzOuvOnjv6cZVElg/kTZq9e2A3hFAKz0wZ9uSX3ab8whe+gK//+q/3+EsvvYQ/+IM/\n",
       "WPL9L5/+mJkq+IZ//W/xr77xv9MGmAiKSpptaQ6ZXLlanWiQsQJTy5/Yv+qsJj3l12VtamOasE6v\n",
       "n7GnpRs4xVlwHAdwXrGlqBAiDIkCTFuQDl8HqzU79FUuEZ8WsXMjrS1uhnhohyxRVsHZ2VNfySrv\n",
       "RlZAsgq82JBsb4Yay/ZlXk5n0yAFkKj57uzfxJwMOtOMbL+y4yKHCbhGEuR51fOf/99+D5//89+d\n",
       "Ss4dA+ZTg3JdQ9mH//aD/wPGGDiOgde9LkYcHnUA86ginwfa/FLOJ8b07CMaKZ76AoAjHDwKSF/g\n",
       "bsCD/TSBpOV3U5jj0yGizCEnq7a8B9jpA2C+x2zgJGDiOPSVLh0IxDyxyphiS7iMKVntwBz4mq4a\n",
       "/k8PCigDkFl9HcnL2jDkyLZmde4s0yEJmNWWPOBTHqTWIvXdse/PRmVNcuT5ClMaULHKXVVX2/PI\n",
       "wPyv/vW/xUtv+1acp+DVVwX/8//0sUvMPDUo3/zmN+OVV17x+CuvvIKXXnrp8pqdjh6qalkaJ0gN\n",
       "5uVY3NTYESrGLNdYEqWTYrE6vMywQcImMbVyqFDrkjuEgBpbDl2HaralMyU0fshcUK6AnPiegJws\n",
       "OsIjC9GfujtWYGoPGwBjOsSOB5LEWB0FvRfWgEfxAKWdr8wZqmzLlAZSti3T/GOkia3mGeteCmM6\n",
       "iNmGTKxOQKY+jcGZ+5zloYCQPa4EzNp6CcCasrAk50mAvR2eGpTve9/78LnPfQ6f//zn8XVf93X4\n",
       "5Cc/iV/+5V/e5F6fZrURsTIimrQmHmtemSWFZdPToxm1AwbtN+qsjcxDR2YQW7JtGQsGJlB9b4sF\n",
       "uD1MrVVm9K8ReOMAOGWakKcAOLVIBeo0JvP8pE6HcO/be5Y1pFU8MwHOmBWQwOrEKd/qCbak88aM\n",
       "1aZc2LNXYcOWXO3Jm9Meus9SmEEWpk5ly5HkbMeWaOJeLg2akjLcRuZTg/IrvuIr8PM///P4zu/8\n",
       "Trz66qv48Ic/3Dp5/Bs9PILww1M+1/Pt8QtAuy1uRA0IzA6FsebKlDe3oaqRqoQT9Cr4i205H4BZ\n",
       "dF5De1NZ7by92nUaMBVnByZgzUEktHcVdR4LARPe+caYmn/YWyMlOKmMtF/ZUcFaX0qu4DvI05rO\n",
       "FZZMjp2VRb3dG1syNJQjg/WO/jyJOVGPCwCtgbYy18mkd5EN+isz3suWr2nxwAc/+EF88IMfvMzD\n",
       "NmPEMxP6cybZk6w+LCPViDymwoJGPVZrIXSOgOksaWzL6WRTeudN9mPbcoJyMmF6i4SZ0gFpTh0F\n",
       "j/8aczh7hrdXNMiwhjl1mDkQYLT2wZj3F8BRaPb0BpQDCFAmu7KCszh6OjDu3oesa10b25LPByuu\n",
       "tmRd1+o2Jcel2de5bTt2OSR1Fp2cNQThcUlp3tw1jcu8ER73NTvJwEys5rYkkgAlDy2XiX3cySKs\n",
       "tAaQtvQuj5hhi3DH25sb6lkttqW/0KwANtvLbUpl0PRRrLO8h+m/tnXomnSZq3gO8bjvRZ9huvIc\n",
       "nL5YfxBbDp2zXLXXGQpL9oDkdavZTuy9sPlYGHiHvREyEtjCliQmRoA225JHAmxa8bOxJdNgXVVY\n",
       "szUNgBey5WnOkpLSopx1fjLy3Ubl4777ihhVIg4F5sgqAYO2GWnSaKcXJdtS5VNUSAOgDEjLZ2wZ\n",
       "ewemeWBv2JbmGDKmlEPmmlVlVQeFqau8PtZeYJ61JBvz6PdqNk7bUmCfQx9jhPrKDeaA2wSyG62c\n",
       "eWDe1aK2NsDMbEf7Mh9ZWVIqcCvYnsKWPJ0l4WhiJw8YqGXqw5ktyVcjd1Z2AV1mymxLhm15Ozxo\n",
       "7SsJC4oaoKezOjByHqpsq0rUcyq4ob7WkbKshVWbA5jTHgHgrCZN+7DaluGpdabklT7QrOB5SkuX\n",
       "iQdjQnt1S4HJ3tfU80PU7vRKzprVEe8eISigDIcPMyOlVU9rBSSl5VU62YbM9mQAMdueG1tyeZl5\n",
       "pp2dLVnWutoxCLhJdrABooGxu8bllommEAxdeys84KfwVGAbxltHmx6QaQQbVOFUnrKkNeowgM4b\n",
       "Z7YkYFYPrIT6mRw+zrCNbelvf4irskOnPwBgsI1pdiVkqnOAAxAC/cByBibO+bSPYf8AACAASURB\n",
       "VHV0B6eYJ3akxkwj8VOCciygBILhbCDaMOSish55XxizTn3wmyBJra22ZMeYjS3Jzh1my5Cdcg3L\n",
       "W7dt5DLLby/biUVvhMcwpQrhpTqAXDkGsmXYjmDu9DEgxn3TSn/qJP0VyK06NBYbs9iWCAADQgyj\n",
       "TGuHOvWR5i0x9HdB/Bbw36U0NdWAqY0QduP8GYN1tKpMCeQfme0CAc/jKGyJxF78fmVWVQNgq8On\n",
       "qKrLEruc19l0Z0sWGxJL/ym4d2tdfc1rD65zI6cdQ1pjVzV2t90Dywf9FF7/QKmyMpZKITXU7K+a\n",
       "vgWnlZOYlRjyBlsyWGFpbFuq+jrtYWVBY0vzxMLUM2XVA7qGlcjJzEnHj6mrpwKXvr5u7Wfqqx3z\n",
       "0GxhCCCvW9o8BwNkUV+dPfW825XHTON49awu7EiMSMBkdVUSIxYG7ZjxJkvO5mSWzIPyCq6Qnwv5\n",
       "AjU1cr6Q25mhn5/MPpVdeBBTCjrXMudhLy2Sqkkq6QKyzebTHNSYWKdFrtnSVNZqY4ZtCb2fezzV\n",
       "noSI2kBwD+v8PmvMWfrXR2h53cT0iN8I0S+oMxOKSUY51zYqYe0yVJuygtLVVnb0XKitBsYFmHmB\n",
       "AAM2gdU0E2fGzpY8yr4B6tV0iK/esT0BtcgT+JyD03yv+p81tUIulW1vhYf8bAFsrnBpnOahkSuw\n",
       "zeebsSPt7V4LS9bj+9jSvkBQbUtTm4zJhjmBxqF3GKS6KqDVdBz82zxEhGILB1QKBk2FTGBSA9mx\n",
       "fUOIG3Dci0h7DjeAi12JpL4mFbPaiptv74iu5OH3IJNqi3WZHc9Vmkbi0yY8N9nNSxZbkp15e7ZU\n",
       "uTSz6Q7WrEwJ5Dw1PoF8G5UP/fKAP9iGNfmHepRXYOyZ1NtlK8A0W9IbcJakkwfTHrTrDJgjQLay\n",
       "pV1jI7l1LVwTmMA9Y52rfSjLHULG/6qGHxLf5WHTzxhQGdNU3kmrBMSiT6Xldk8KSAuD5l93oAQD\n",
       "srEttyrrjjH1Ov+Oa6iy4QTKtuTKlpUlCxvKaOxEZsuZdvI5k18QWyYZBgFMcnq7ZbvzKjzA+4oQ\n",
       "Jten4skCkKOpPILxqjw2I1dq8EENNIgRaW9P4p5Zy3uPbQkSXP+WD3ljdUCZnlzNpi0g1cY8iDn5\n",
       "x3yOQxeox0IB0FPPwizdQGtt/YRhcfCQ4dsy5ZFtS08j4KVldhWQwXxpPjLZmArWO21JCPdnGbR5\n",
       "v3j4Mztu5Qy5eVv21DutNiWigBvhy8+UmKiaz1MYj/a2ImWrro4bDcKqak0T6xBa4ZM6GGpfdmoP\n",
       "25ZIaqw9iKmmMrx0AKan6gMr8GKlDwMU2cbkcfqYg8WwhQLjyBU375fHXwMoLwFpaYe/4VHBKlVl\n",
       "NUDSnKUcGZxpOZ2zJWkl1RF0YUvWeUovJ8nKRn3t0uq5JK9FPrW7OjZMGtsdffMYpsSCENQld11j\n",
       "2HlI0yDF4ZNsS56vtLJHKJ0+QLD6aiOxyJYtpypd7EoFGBAqsLtU1QE0P7I844sq66DT9joQUyI0\n",
       "yspBjYRpv6YRa4gvTPeB4EkCgxJZbTUtYVVTKX0BJNuJWRXN84+VJbO6mkDIA2lhyZPjBj5mPrYn\n",
       "6zSJpyEIJMnWHfLYyHHkp5N3hIevfY2RQnKjscz5tZazxJuRKuzIalvSOWPKYZ0kqbNOB9CrLVvC\n",
       "VSiLi9ua/DlKD/6VvZiDFCM7XzFnTKk2JvSNEhjrUcOckT4/cl3O+/TIU4bGlpQE1M6G1MFqASQx\n",
       "pcUPZshgXtvYpkxTJaMAcmdLLhuB0WVleHPFAD3WczuCAFKeJI9FjkURncu83T+PW/sq/o/AmVGX\n",
       "Gq4DXgLgnekMTFCDLcCcYD5t0bkB2dmyTo2YvaPPzvOSXqn42TtLs+/+2NfRx2k/415sTO9VRbF7\n",
       "ZY0NeY88hD8NLhebEnFcmdKX3QUDZhuSnUEdyAY69TXmI+v0RwHkwpIELgALMBmAHK+y0qVdpSdg\n",
       "kqNN4m5+aHe/o28etvbVRyvY2LECDylepjmIaU1j6xoLCXysjlI6O454RHWgdp1bPH8EUqiwAJOd\n",
       "tebeBpEkpLqeBERoi0AZc56fWqnakL4+tgJS71NB+qShUV+FAbkw5aDzxYa8UGH3C88bcNq5C4Zc\n",
       "1rsuc5M1nZkz5MJktYJxTTe7cPW4GuYWwDJb3tEVj5mnNKRYFA2YSqX30yblGgKhnYdd77altEw5\n",
       "5+1XtnQQF9vS18Rq3Jly2EBzKCjn8dIGOn8piM9/TGcP2ZgwppwPKgrC0TCl/b6Jj8TcUE8ayIZ0\n",
       "m3LDlHLktPU1rI0KiwaExwaYzJYXtuS6AIABS/2N0v808IKabcl312be1twNqTvq/iI8bp7SBB5c\n",
       "kRHnLY0YFHaNELgkAN6qEh2Duk2JhSkDmHC29JU+lkZbzFcGc8LVW8SXAzQMrf1EnAHSdAX9Idjh\n",
       "sA2g6nnzrhqDomPKgRx/GlxW9RVYAYkR85OapwVg8rAOsAqb3pNU8J2VJQ2Irs42mkq3EUueCzNy\n",
       "HJpnP+CH2sl5MjtGHCV9TYvB4HbnPHCeUkXNUOEnuQFs1LL0sR19eC1su4HzDgdCa2M2bMm25SlT\n",
       "oAaDj2swqNPM1gLF/Z1KaYEnhzqKBPO7P2d4bB3UzqClQfhrAxa/tQ69hmE3KkxZ1Nd1JQ4IgJUx\n",
       "B6rquqqo4dwJwFWmpE2munr63vqZWZL3DIYsDztZqelnaW7t5gLUANoyP8kPYfEb4XHzlMSMzpqS\n",
       "n3VhS71eVOrDg0qNqviOxjRmLZ1i9qIdc3s5IOFsySrQQfaLvT3iI/cwpiR11uEUjiADJRD7QTnj\n",
       "9ymhU5ESJqMuQJ+qLoNRn9oqaedYc743NOrr4nllprQ8rerKAN2BsrEdK1MWJuzel1xZcpAcNGou\n",
       "WE6q3BjQClBNRlw+OU5ya9dWwKe8t1H5uHlKpxPWL5FHIW0cH1CaUWrLjJ3NKNDPd0iw5SVT0rEM\n",
       "nGPoe8TaqWOO0odPFRxRJRs1E1PSwEigNNaed5vssDKoqbh6nc1nMvh01RK/KRJrY5+gjxSQ0rHl\n",
       "jil18FqBmBmzHsuo6irPSRamHPTi8qUtSYDzPizyoHtnye48x7sNIY+ga+DXFA9suhCB+BvhGcxT\n",
       "Zpa8BluIqdmUuSy7R22Dcr/Be9xgShS2tH0dtQ8ciE9MBlPqDVRwbe7zSLamONgyAG0/lDmhWj8N\n",
       "F6az25xosSetHJiFcG8/2TRIsSurBza8qBmouz3PS9pqnoUljRlbpqze12aqRAfz20wJOtftY8ty\n",
       "VVjSWNHTVwy2siyGh+vwsFe3XPV0YNJgzkMOMrhWJm0qXeOdrYlyDiC2ZEBWTyx7ZG0/5zGqAwIq\n",
       "OE53MGychUHjfa3EkMNUVmHym084Toi+GD3oSTkOBaN1fFaPbwRy7oTaGvFhTKrziPYl+JUhrQ1G\n",
       "AV8AKlT7YMTLBQFyNOyI2LfXRd8n2/Me+Wk2lssktsaO1v5ig6P+SXhmTY29FR7z8+pJZ9Q9kAGH\n",
       "2w3DoNPLFxCeRhoLW1IejHASWTlg9RXBlmKsqdMhOCAKKhMQV2OdyYhJ7jLwJBjPazYZc55T1VVX\n",
       "3pldaZ+UTD9o6ygMP9+9gOzUVwOoWNynN8KZcw3KWxszZaivvmwusSQDlfatfVjyOiB7ljyFvLGI\n",
       "fZKzezbrRh9QkQt8HpgS0NFkp8Li6UauDqjGP+6ZTWUr6ykLnoaDwa90MUANzDTquvqrKqszJEJ9\n",
       "dVBAhdrWse7Dqr6GzRmTNtHHV0wpfm+h8q6AyfajllZsShk6FUQ25Gy7jdrazUfunDzV29o4eBiE\n",
       "ZwUb5Tl9i353lqxyRmnbPE8IxKVsT8vq763wDG3K4kW9sUV5NIrdbCS+j+TzzoTUOXoPn7ccI8xA\n",
       "+y6PXgsXBLUtLY2ZUmwxAf96D7QEU+G0ImXvDh5nvcMwAls0YDZlimseIFz1l4JgALQ7b2zKtDfV\n",
       "taipPShHAWhRZ4sNGR7WzIwnnTvFwGl9XOYlqy0poDxAZcmtzBXAJfm7e5Nlfys8aJ6SH3CO32xb\n",
       "tteAK7ZpPGwaotqUIzplGEjtfUuAbEsCLOZ9J9uJd/Cp9HqYmqaAnBMax+RFZ6sTIvbGCMDgDAWY\n",
       "Koxwa6Gmm6dVLJ+kfDlu194xLhdQ7mxKfiMkzrOHlcCpr3dJB87FlpznT3biOAMemR15QF2YcmWo\n",
       "xZbcyc1Gjs4mLYOtIBhsQ5pNidjv5L2EB81TAvGbiYwaFcmrkSo1wkC8d6nff6OG5bJOmEOyYUsD\n",
       "KTrb0ptXWY9AauyhAnPinHOYYgJ6zmcjZ4/YzxLYA5L8g5jQqR/NPiYs55Okt0SQ4170zHc7EAC1\n",
       "bru5ysySF6B0W7Gosf6qFjMkgXEEEIM1G1vS+hV0XBkSHN+zZAKe9f0id91e+7fk566Nk9SXzwMo\n",
       "nSlRKlpVyjKaoTTKeRKAbGNA1bRqU1a2HJNb2La0/GZjQibruR0KnreEs4bx3YmBYyhYZQLzFODw\n",
       "r2OpaksrfKKRdvtBd5fk5AmvX6zgzQ3/5KBcbMrEjCNAR+r6TVAy6HQ7yZY8hw1ylf2KGkrmg6ux\n",
       "IBuS+jvZiRV4dRAm3FxqYEkmQ3NpzxtrIgP5nh55kKMH/iW2AB85e0rcrtnmAXtV6zVdR1S2pDgK\n",
       "uHkbdD3nRV7pY6D0eUrAWRPjUGBCS7WXl2dcRD94YXYgqqNHUn5bmetPb/OTYyzvcuahexNamxIZ\n",
       "hItNmUFpi9TN63qSFzYzJqmqWkYAsp8SSat4tjbjLj0G4o4lu83lSHtjx5IcT7K3ycNq7a3wmCkR\n",
       "zIbw1SYA3E0Ykg4TPieArOvdGL0IjDtGdbZEvIa4VV8VjO6xHdRRqtrJHPEx1EoU/aQO2Zj2G3em\n",
       "4toX1Cf6bGkdfZen7Ic+h9matIq3PCmURb21QJE+mOfI2lnj06rQNb7k+DHGnICyvOs0CEzt7Bw6\n",
       "rqZuVFPMNj3lKOnIebEH101bssrSPbLloM3tmuYpkyBRP4PTr7sEeOAX0kOUGqa0cV9yXdZRpzBd\n",
       "N72ya+jClryg3W1LlM3ZlFjVhFbgrDIdQIcDcwpv2JjAoWDVh2I704/to8v8KRDQHunpkrrKKw3c\n",
       "dJensimT+gpkMBIoYU9xHHENOW6SU4fY8qw2pGRgnrrwvFVfl60CtbAkntzj2jNcJ4vk3U54JAcP\n",
       "X+f9dbtPHvTdV2SmFMBdsmCDEzHgXDQg/ZBxz4h2DCp61Dyk/kL4basIwxiKWFIHD2NKDMxpETlV\n",
       "WHV6RDDXzhrQHLh2I7UztYzMkNx5KyhH6eCBaWt+6dRXUslJbV1AyczontlmQUCyHYeDdF1gPgHp\n",
       "qqwx52JPAqba2qQ/b3nwL4N0FrXrgVxl7RZ41xtZY0rsSbZvhYe9Tzlgo0plymo39o3DjApkuzDi\n",
       "BZhLh2S2XGzLZbNf+GBBwFRXBe6dnRjMK31miDT7Ct2p34ZNNqaxJ/3WJfytEQOhvYdZnxLNk+tD\n",
       "+rmLsGHJDpSZEeGg8+/qEOBWGzIDtvWsclpx8NR5yPXXtAqDyhOyJMkcrJWNCSl+69orps39sw8P\n",
       "WjwQDRIVVhFzYNIjt88e1OeNd0cDtyzZ2Za2+W0KO8JgYmWIvjGizzGgcZ2rdBvzUOuMPlc3Tiw2\n",
       "Jqzi5vs1pxFv/Fn1eEobmNJXCDhbKwgjcEtxc+BAS09vhBj4RgYSCjh7G5IBqCos2ZCCw72pmSFB\n",
       "+fi+3Ee1z+9gyZ3sNPKV5bH0iZiXlTyuLs9l76C/Dg+bEoE+6JgeiRUllnc7+pDn1dixMl5nWy4d\n",
       "k9kyT4nQ9Q0kzDIWVl1lelbdGysz32Jjgj7G4+f1oZQl+Qvr1b2UgYvNk2EDzEYSCkPCnT72vB0o\n",
       "Bzl2AnAgtbQC8+TXshYbcjMNwiqrA7MBm6cxs5oa+wQsuciZ7rUV5v33LNl2kZ4MD63aoHeg8mGL\n",
       "B0QpKCp8AShsQIU8gm236lEt+E97mR/lgND7lnadM+QMh6XJ9LIOsXlMfaYxVFnNNqYtxXNgqmOH\n",
       "bUwbanIPr8MC7+sQFemcbxMKS8qXCJTuhU02pAFRp0GYNWWNd8D0JXYtY0Y/nzawLoPxZl+PZV3J\n",
       "A8Fyn51sVmDPhnwemRIhdDFqNV7U2qBLo+2uacA9muuXvV4zeM8dQB5jjZ/KKofAmRKIRQZR7TzV\n",
       "kYBpn40U0c+OIK3OgQiptRbvvLIdWK+OKRAIAWSPq181IAsomQ2H71EB6HtWWRmAdZ/BuABysSFR\n",
       "4sGUKzteyBU4bedxLXs0Zd1RRkjUdXjY+5RDG8a0ptw4xbbcbk3j8m+ols1sRgD+maAJWANh7iBX\n",
       "ZX0bypyijBk25UnAtPynzPMY9jVItTmdeepcpIZBUyKintQyNKwsOpq4tm0FZWJFDnRi5ExmW/q0\n",
       "T3HkoIKSATgq0HoAnsSAzIZS04TPU98Ueehever2yVP7xJtATrYdaUO1IU11JSzcxuQDfwpPRN+r\n",
       "RBw7jWbbsgXe4FEns6Mvndt5c1vWLEyre/+6nYFRQhC0Ng5Iq4JBB6q+Bljnkjtbqj6/EknArPOL\n",
       "DEhlRx/I/FeAGIx8TO2dUHglBaMcMrBXhpwlHYUdjwaYPA8ZwAwVtIA0gdP6l4BZj/084B/SWgbu\n",
       "a5ZcASmavjLc6fE9aWTanS1o6eKCp8c3wuOmRLxi9N4iN4iroejnIE+4eule0zs2z7uzKZd92Jj+\n",
       "4Brsix6HCqs5eXzqRAaOMWMQA+9wgALiIB26Wmeoj2XIgTFOhQUNWIkxoa9rNecdo7JhxioMXabh\n",
       "uwWUwKK6ZlAigFa8sy1TFk+reV+jtgRA0JfrMIe0E/S6lt07DboX+yR7V0Bt0hqWnH1jbBmA5lY3\n",
       "OX9OmBKwUcPYURQBUdmV4YA90LCwooHigi0vO6phTXQ2JqbACvwVLbseeu4UAEPVWMBtyXjVuVsk\n",
       "YCOHthWmjWm2poh43H6fZID2IqF93rWKZxfIRUS2JDt+TDWtNmQ9v25mU1a2jM9GLkyZgLt5Z9Lz\n",
       "X+1vbXfakk9cVrCrDZzPCVPaEG4Pqgun59DrgggHUwz2DFBotrmjEdVHMNxlWyaCMSBbOdCOBAM0\n",
       "oGM25TlEf9tVGVPT7cFFhqu2FgcQS+0MmNE0GspqnmELC+bdk6PH09n3OuPDK3l/CCeVDTBWygi7\n",
       "ktTTZEMaqzY2YVVd0/SH8D4GuLwIfdZ8dfBQf20A2K32eSJbMjWQCePGnjTWJACygDJgb4WHeF8F\n",
       "omtLg8VAD2nsNjDCfhwhr5dsiSewLbHuTzcMyUBEpBm2JjOKO3O0e0Jw82Wzg3TFD89Z+ktcY67Q\n",
       "OcRKhzuNhtExZM5dAgDPX8pk8YEAI3Ec7Z+kmwKUsy4jpfNKn7Ah2cOq194CorEkM2MFaPWuuiob\n",
       "bHlK2JKxR0rbgbQy20y/3+O6tN0JyGngq0xJx3f2zYPeEhk6sE+JnY4eez4TwJkOgBw76whoI5Ad\n",
       "c2MxK3YdMguPvbOx701ITHWVmKNUVdY+YnWSt/KAuK0JBaR9M9aAeg5+0UvBONjGjHMTjArequY6\n",
       "QyIaQO3agVrJJ+gnMAhjRMyqqYKxruhp1VVVWTde1bArue3t3Uj+3s6IPjJQp4H2WlV9bZ7Wtekr\n",
       "oPMKHhf62Bs7qpA9H0yJKTDwUU9INWVGs1rVxg3GA3Kav6ws7Cjq9hV82mEwU45U1ZpPVVSzW8Mi\n",
       "DBjMl5upL5QhWYX1vYbVxuT2itW2OkSoTSlhY1pLujlb0imwW+i6nwJwu/TkaU3ARIpXG7JXWQlQ\n",
       "pMaeLhvEjsSWK6NWmbHrboGOPavrHkt6lcsLgNLe+jDi1+FhTKk6GJAAllXQSQB2EojlNcpO/nZI\n",
       "dEIV/iu2dLCRxzX9Jgl7YIXQpIOFv8Ls3kaNiy1UFxzKDAeVzYwJIFjIgaoQV9AF43VhhBqbG7pP\n",
       "p9te9pM/2HAbcklHAO/KhkSJd8fmwDkJZKtHlYAu1rebN0PKYHqW+I5FEytSnddr2G6UnAkRn6d6\n",
       "MN/XEw9ckD4cSLMCq42po9OgUQ/GXiMqnCo7SCWOis/OFr0nsSUagPo+2NKnPSC+ztXEfWVJ+6qA\n",
       "drQDMz6gZWmOFgWjMfW0Mekctx+zprMkYCAxjoriKf2OUTkcOnE/BmFKHxlclr538HSABAFyeP8m\n",
       "Z46zYmHLlhmtDDTnrra9h5WJYDs/mdjPgFiY0vpGM3nZN8JjQOk2jxsqOrCr+IiO75YmgHs9BLA3\n",
       "6oMt9w0/77nZRnPcsCWEFEpL0LnBw8E4b+YApKy2LhYwphxbYEY7DYwhuha2bpF9pDlKS895rQ3G\n",
       "HdMjrAJ7nEDH6VLO12MDW+TvGBIBTIQNybanO3OAOA+LK1NiPDlLXsnGje3k+UliRm9skj++WQWi\n",
       "cGQTHjNPWUYf1wqL/ReLBjLDQfIUSR7tMkCHqslb25KBiXVvv806Swn29Hyg5XawAWOQQwiOIB8k\n",
       "OhszNU9MY/Cnm6Opqo0ZBQwf7iR1+NCfW7gZBpABmFmwPmdlSYAA2ZxfbUnQcTClA1NKupAtud2z\n",
       "HboBFji+2pJAd93KkFjOUxkcBzNmUXtvhIf96pbZjZMN4Tamg+bUTj7geX2Fjwq0DfzRKKM0Hqux\n",
       "6nG167sOQqx3nd7ZgUNiGXnkM3AOF/wEUGNyHc3NjrT5zGpjDt5jVV1P97wGIG1vW4SdG+de984o\n",
       "uZgBuRt3gLT2qSorXZNAF/lNZeX1rZNFbwCsbCftu+NdfpaVHmgRt4QFfBW8Z5zz9i9AvhUe8+oW\n",
       "9Pus/gM28b3WmFecDzynSsLGZLZMLNeCkdj1ii0B7/xD2As7y5pXz+eNeUyr0Ug2JSABOkwQAnB2\n",
       "tHWy+SPNtGdKTeAciGFgOPMNmIob7ZvZlNLLIvO2f4RvbGAL0Fk4GZDSAdMUbwYoCiAbGxIBPp9f\n",
       "JEbl+cllHtLKuBOMWWY6Z8wKxjSQ21bY0RpyZU0VHQb0HQPlw17dsprJMMDR72OkygeAQA1V32Ra\n",
       "bcusyvotu81wMPyx0jym2YemyoZwhePHbUqtT6z2sTWyoueC+SCVKfVnYt1RNNz7ahBwptRzwARI\n",
       "ANBasXb2fUy5U1ErULNNmffMiJyWgWNpGbgWr6t4/FwadPOWbMcrMHKeO765k+5xZqYMWS0ARgEy\n",
       "QlZDJo1Br8PjfuBH4GgwZ4UNHGEvFhszVYoAl65ZARmg3HtiTwCHLc2zssoegAsiz4X6VwaGjoIK\n",
       "gDSPaaAmbHQ/9cNvnBhwHaRFdbW9MTVgfBqqroVBeW72TwPM6uxxppQNMIkdwSopgABgH+dVOt7X\n",
       "VO76ycgnU20NiGcCzwrADpgVWHVqpJ2XtHTi12RX3giPmae01TAONB35rdKuIa6qJpqGSm99pE6i\n",
       "xkTuOJ67PE/g2IAxM6ayYzpvwLPhUL2mWol5eUyd2Ocr+aVoY8uYMgn1OWxNAqIb03PnX4MdhuFQ\n",
       "db3dFUBA74XdOYEWm1EivYIw0pu0DTPOAZHtx4EMMmJPCQeOr/wpA/W9a1qvGXKnymrvExD7a9fr\n",
       "DY8RZ9m8Do9b+2rHYutTJT38ZL6qjsJt0NoYWBom58MC8Ng7YJFBaTZmSsdItuUhoaKaSjtBKPpC\n",
       "FpTNhrLg7AVfdkeBf4vLAMlMmdpwhMrqQBTm0AAUEGWY6tt3jVNyk253C6hX4Hmat4WBuLz1wSC1\n",
       "tmVHj/cdg9jKDDXVbcpFVu7ZdrZkBZrKZgviHUuGvECCFXNeRMYb4XFrX1Xg7OcLzMHDbJm9qwE0\n",
       "1MpLZr1qW55qr7ZrYI0lGXyNjen7ZFua0PmPn8McP3MS3goJVTU+wgz3zJpNWdlTJGzNKcLq4AH/\n",
       "JIEy8mCGXJnSDhnMqV+ISZd0Yr8oixjRAMlqpsYjfSTgBTAVYCiATIy7d+gwABbQ4OLcZgt2Lbbk\n",
       "Ar5rlrREsfYy/BVg3obkA5ky2HAKnSAAGpWYFchL6di2LHYjlRmNpHYrVpY8RSf/CbjWMQCxJPJU\n",
       "CS8Jt3QHKcyWjH1rY/rDsp1W5iTZN+POH5oy8dO27jc7cjsb0tYH9/1yhwpb8rEzBgRGBhQ2NqTJ\n",
       "blrRo/3K7FfnJa/e+Kgq6zItcjLgOvuvSzd57DYGKgEPoDIIiNbWnH4jPHaZHQuRgNgTaXiz567O\n",
       "nTpa7WxLT0fTqFCgSUyFQCgv8lSJzTMaHA4XRnuDJAPSPKOHMZrm8a/fKataI5wynD0dXiOeadjI\n",
       "oUI9ZnHRhmhsT27/xLI5ve+vrJYCcUOrSwCQbUhEOrOiO32izJ0NyQDMn/ioQFz9BT2A7jgPk60C\n",
       "KjD4brAlSoGpbKF2dDG6DA98dUvcPjSbkpkOBVR2LRAA7L7hszYo30MdNcyWmE4Z86ZWgFqbLVMk\n",
       "CPuGQWiCCGbKEazMNiYwX+maC89HWkRgb5ksiwp0gDF11sAIDP2eDzf2phM6orzD0TOFyuJY0mUB\n",
       "27zZak8GiK0NOxsyvzOJNq3ORzLgPH6uamn7vqQKUwLjxiHkjVBAinKfzuas97gVHsaUpgaFFQQX\n",
       "uGBL8Qr473g4QK1S9juV7AjqbMtZroNNij3JXypQPdJU03hevY7q4wwKY9CZ+VAETe+shI2pQr0u\n",
       "Hphq5ZB5rdmVLv0FpLBL2RRsbM8a7nL0LH1WbEpPj+sSU5KtWL2u1u8ByOzESYAscQZgt7+bDc8K\n",
       "1H3+a1ty9aAasKHnM0tGHuPL5wKUHNjmY7CGXTi0Ytm5s66JBXjKI5eR7wOyLQHBear1dTB7qj1p\n",
       "IB5hX1abkh7b95ZvwOYnSZWl6RKLD1ZZzZFEgBUEW3rbjahjggrbnl2bj026nezSSc3M6XFddtyQ\n",
       "BrPYkmWv/bjYkGCg3PasJoBhdy6+KnD13uQtWzIAank7lZaBuebxc3eEh73kbJ+XDJ17SpHZmvAK\n",
       "xzd81hU6AjlVfToItIHj1Kk+UtXRTfK8JeexEU6Qp0jirRGoWhpfcQWGYOSrbAAAGzhJREFUTn1w\n",
       "ejh9TmMzV2M1EBDTulhNNI+0pWvWgtZI7wiRVfK1X64dQMnBQ+XUeUdPQwViZsW0aLyqrIhz1VlT\n",
       "5yPvYscn3m7YkmlNawYsKri9HQsgSSavwgOnRObTuCdWhj+4M52zGgC3CxV47pFVtRV5NLURbqqx\n",
       "UQYQ3+7x6QQJDyxE3J47df7CgDifP9RV7wMAAL2yxWqrKugAko0JBy2CLRuwCkCfnaR2RHhhdTxL\n",
       "6VLyd9flfgE6DrW68Xmhc5aepzFm30D3MQ1S9j7wNV7VJW119CQwnmsae1oDwCsrrumyXVxgbRXx\n",
       "4l1NgEYCNOicg/QOVD5OfXXghONnyquCcyC9sBzTJaM0iDVQb1sCIQDMlOmVrK6jYQsCGHhwezOE\n",
       "L09l+CtblH76JyYrWFXFbZrnJKCazW3OHmNLA2MyPSm9624fD7ouueXsKeprDFRVfQWMYQNgGZQn\n",
       "9YnH9V7+jiUDrIKQt4vVOU/vib1lS3be1wCmCYe1xWwnCblHHN8Kj3P0uEMnWNNp3Y9NJOGABDXE\n",
       "Yluq98RBW0a2+S9sR0GJi9mYtuzO0tmZs85fWroBTIC0dA9+PtuWVm173UvEXvsi4SfHDuicAbqS\n",
       "mwNyZzvKhU25Y0oFzMKUwuezY4avYyAClRHn+bxyJ/qVGWsLTHRzkQae++YnJ7g1/wJy9preY0sq\n",
       "B+7yKSD9+EZ43DI7lRpnSFd3JGxLmULoOBarzMa2POx8BqV9y8dWe4cdY9ejlMcCEwBL7Ikyf6ll\n",
       "8VylnAPnIcGEMlkz1FT4a1c2n2n7gXACTWePTt0gpk/cxkwdO5LNWcPO1jRm67ss+iCl0XUinDa8\n",
       "7fqpEAMQ5aM+cdCdka8DZDdv6cc33/7ogXcFtlPutCURZbqa6ifiHs8VU7K6ChAAAQeoKW0OWljl\n",
       "97blKdPBYp2c1NUTOHShqgxrvGxTmkc2QDlwnoLjCKFc5i8LYLUKqobF93mmyikKxFAu3c4UxBwI\n",
       "2Zz2f7j9CR2J41U3thGHPkBN9/bH3tZsmVLgzyEpfdB5A1tnUzIQA3hnd2x5rM+knuvmHXuAdp7U\n",
       "PVuKDgCdLdmrqkBvS4LSZv0lAbGy5D0e2IfOUzJbGlPaA4/B0yFY1sp2tmVm0UAOd3iAMITMOgxY\n",
       "5y35/BgKQL3Q2bEA0+1KhNDOoOqbQoq/UKC1cBWXbc64fDaEAU7EnFgj3WHQ+Rp2tua8/4YpZQWl\n",
       "pcPr2E972AARNiSBDtxfVaVdAdcBMnlmt84eStsy6I4pbwM0AdPqbOkgWaQyOH4rPEB9VUtOggVn\n",
       "soTEGDAlV+iWbVnXxPI10Ujc+RaPPduQkFgbO3VqKgvZjmTbMn25VcHsHlS+xm1Mc+Cod9hVWOg9\n",
       "aT7TNAhEc1UoCd1naf6L9J1NGcvnSv4CPFZRPU0oPamrkd6tZV0AVwB57cBZWbJP353vQGjAu2FL\n",
       "Ut4lf8eStzH5iM+B6CSBPlCyJYW8rw6QyMdsmVlRy06jUaiZDFZA4ovrpL7avpYnIE9tErRcJ5xq\n",
       "srLtiZinzCHPXw7AQTiQbU5Te82AFLcZbUgxi1LofcoA8nrnmKKpZ7rUCsjZNp3qmo8TAEF9VY6v\n",
       "V+MoaM+avtmwgvk2YLOduKqk6+ayIXHgMpHAHHK9Y8nniCknCJwt2RMbvesVA4MT8LTVtmQAaj5/\n",
       "oVobyITmxHQMJaakewLhqDFPrQmSzl8G4/WqLGALC5glDaQBJmi8P4ZzowHV1NyY/hDE/wBm2/yb\n",
       "c7dUV39SyflDGLNzp2fK/XFaSEBpHTMuy+ySrUjgW9I7QK6AnTJqYMssCVzbklcOo44lnwtQTkdP\n",
       "HDtbbmzLWNFzj21pgI2GtleajFlno9r5ypQhGADiEyFj9bSKIs3szitgDjqXWZKZMX6fxADoLzsX\n",
       "0Hn7gUBodbS7DGpLCjHJ1PTNDfXV+8VLini1Ie2as4tL5O8AecuG9P5rpkv8mrtsxwoeBubu+lyW\n",
       "AxN8TcOSBMTMms8BKAF9DnUTXtmW8R0dOFNVtozRKsrOtiWXDSSbUh+k2pqxsEBfXi4eWAG9Gyl5\n",
       "OsTZs3H+MDitExkHp0fNtrSjUFJZxeV4wNbKHwli2ZXU9AnllJou5Vx0hR6PLJg7prQ4b5S2gO/C\n",
       "hswqbWbJ+gbIPZ7ZBFAwUA14d9qSaPKblkVlO1CbvqjhMV+z8+83hlrY2ZZB8cOBnN+7LOdhDZvt\n",
       "0gR4cCcwU87z9urWss5TeqAdJ3AeeVWONXQ3XTKP7S0QtiOhr3Ahpzn4AkyuvlpzwjSC7IXlpxHA\n",
       "PzG5symtrrm7yhylA/JKfbV8GzCmgXHGuznGy2V1stqOV+y4gnenZuLi0x8Rt4Nc35x/ZcUufhuW\n",
       "D/nuq6mrEFH/xQ3bUkeXQQ3Q2ZaAAVSSbWmoSHNn1nCIe815TiR700DLgK4qqM9FYmNjjgxc8b1N\n",
       "f8BQk1rK8oQdycwYcQGDNuo0zH1L+aLE2i+aS+L5or7xvHxeUNq0xCO9gjBU1iTMG2bs06SAtmM9\n",
       "Zc30qtaqqmZQ71gSJQ3lPB0vTIuUDrr2nvAgppx7W5HSseVqW6p9SdcaWxo4J4CskY0trZAiKJaH\n",
       "mBICnPbelOS1sc56NMWBg1RVRQjbmAmkxKjs+OHpj7ytKmo0n3hKBqY1LugKUBmRa989mRmr3LA3\n",
       "lgf6FZyR7qATPr/OS958T5IYdDs32bCcva7VM99OLa15O5UVThJedwJiDDgUt/PI116Fh6595c8o\n",
       "OmNtmNMrRK9oVNsyvynCQDTbszClAtDLtLjmFWIdJGGN+LxUeWusQryouoMAjOoESsW3SSvvMTDD\n",
       "Ak16PuAaSRoVlzCykNHNfXgI+fK2dHscUX8WWD5nxwYqO38LkGe5rgdYji9fF6hrW8+szqIAr4IU\n",
       "6V6cX3xaJYGPKu8sqQ3q19+Byod9jBnamQasIQKbaJMRlYsPXlnl4EBdbEtjUW7EeFVjNsAR50VR\n",
       "ZJ5VB6/mPcfAcWQw53roHvFcrLp6Pt1Xp8/wdGI9bYY8BZJtRAE7d3yIAFI68yww6DpQevec9W0R\n",
       "ries3VI80hMYYW1dbEtPb4B319axWZPnLPsWbIUd/ZqOQeMGedDp8lF6jGp+Leg5b4WH/RTeMN3V\n",
       "g9IMf9+CACoyJV70NwTcIQQD4Lwu3hwB5Z+Fia6ICSER2Dcf09rYI16xsjcVjiPsVrY19TF9navF\n",
       "OVRHT1VVOxB3r3MZqPguAcy8FtaedWgjzbqvz9bdw9uehwIp+5KvgpFBeUqOC64BeN9qnRqPdH5L\n",
       "xO3Iura12I9Ao76SKpwHGQNmAbcB+czALGqFtp7d5EaH4DWA8iMf+Qh+/dd/Ha9//evx1re+Fb/4\n",
       "i7+Ir/qqr1ryiZiDv1/vCpF4i0EUvCeI5fbzlrOcsC29HU4ktdTOm7oHz0tgOwVy2IJ0OJBzXfwx\n",
       "U5yBtwWjAINszPpzd9XWtHS/N3Gh3X9g5b8u3z2hY0sTyi5fPR/xdR75tP2Zr3sycF4D9zTV9Kyg\n",
       "vbIdQdeUDfGQPAChlm16NhSQUNm1Y69wznMVugH6rvAd3/Ed+NM//VP8yZ/8CV5++WX89E//dJ9R\n",
       "6GFl9UhxZSOtVyWW0cm22vjL9UDfMV0HkpCcfb6wg9aOvhQsm+Q+i/PCjsvUwCk139VnF2u+J9t2\n",
       "ZeX7rPlSnS/qdevVqt5hk9t76Yf2DY+L/tzJVCcvSb6yeovN9awaCAEy5bkjPDVTfuADH/Dj97//\n",
       "/fjVX/3VDSbplSwFYHpFy4BJbGl5YlTKiwJCZRrRCCf0Y1ihJZug4JB4/9LuAWBd4WMsILHg/Bzx\n",
       "toipvJjMNj2skry2xxg4j15NtdCptFOzjq/8+TuSw+xOba+xLq8Tgc+uJHvmiUO2pUX/ebNTu/E5\n",
       "4fbOstmDkNLrtIeVkxcTZBC26uolMHlQD7kQlTUnNgPj1fWUnplTgYf1GpRyboUviU35iU98Aj/0\n",
       "Qz/UnvvL//g/zoMx8J9/zb/Bf/E1/43bjeZ1HWRXmprrwkUNFL8zB7UdNc8JiKqrbnOaUFsZ0HnJ\n",
       "eZN5L80Y+3nylEFTGpxngvQYAA4hYIbDhm1NB5+BDPGlAgatxS2vOnaLKqsOHJE0vcnAnFn6FTy3\n",
       "gpQDjgfICLQFfLs4e10T+yKOF2ChAPJs8og0q3yumbKCDInBCktKE986gzJIvZE0/f/+u3+P//S3\n",
       "/x6uGd4Il6D8wAc+gL/7u79b0j/2sY/he77newAAP/VTP4XXv/71+OEf/uG2jH/17v8eADDG4Z91\n",
       "XFbz2Ag5gkUdqN6Q1R5EaoRodBPeEA4H8SnkCAJWpgRsGuCE4DhHvAmi85aAvmrFq3divRyAPI9Z\n",
       "DT/PKnOMMbBKza4JxoLBhvqsVKx1dI0/TagDeWVHZkXbS9l7egPAurGqiy69mBCVLW/PR1ZQYXXo\n",
       "NIBdmTHnqywJ6xUDOwH2q9/0b/Cf/Zf/tT7DGUS1CZeg/K3f+q3Li3/pl34Jn/70p/E7v/M72zwG\n",
       "MGM+X07nDhuLD/Cn+zmPj0R6OjywOS4ydC6ShCsJkZbrK340TecrHXg2f1lYMpwhOd3WxRpQds4c\n",
       "VnPHWM+jxKvTh9PR7CsY72HMBcBCuxgDHVwo+5qewEngsjK2zLmkdyrp5ridj+zUzwvgkdqKcq7G\n",
       "F1WUKj4PJQCbiORLwJRX4TOf+Qx+5md+Br/7u7+LN7zhDfuMQqP6uMe2JEaUbFva1IoQWJkRXc3V\n",
       "0ZDR4V+lcw+wMSNg85eaDKOo/P7lHJX5u60Le1o6hADD6RlUNa7VaOOcHl/yQ3qnMvX4wF0C4Ddp\n",
       "ogwmS1/SZE13GeWtS5O6dC6Dbf2ywBPYjgL/FeZ0TVVFF5U0Bgd+9imSwX4cfyJb0vYX4alB+RM/\n",
       "8RP44he/6A6fb/mWb8Ev/MIvLPkmlkx6DHgGLgPkfbZlioNsRrIfxaZUSE1No7s3TtiQAmznL9nm\n",
       "hBjgYg0r25iVm2z1T0qPohyQzLKZixtAIupu9R4NAMf6OH2Q9VqgCuM+vQWnxDRIEnBKuwRkdfAk\n",
       "8BUgtvORHcg7NbReIyqjPUMuIPNrqGM4H/I19wASeA2g/NznPndfRmMcfSBnPjydbTmIGkRU+ATp\n",
       "K+t629AhCaRsm/onKucVMSC0Xlm7yTw0WxPINiZV223O5OwZETfUmW2pRbfg3KVvm/3GeX7OXbqU\n",
       "8xWEXb5W6Gs6xQ1Mdu3OhoxrOobMYLmpul6xpFeU6u7PJ+ncLVsyk0BhzIvwoI8xiyFNwYhQZTe2\n",
       "pWnfT2xbFnU1GhTU0MZ6mF/DQ6RNEM64fdnO9vr+FWzOZWdjsnrpN28+NcdAY+DW8345jQsJqA0C\n",
       "vW1uITd2Kd2aNTFlBWBJ6wC4nDdw1Hy434Y8z7yvTJi9sffYkh1AM8hWW7IwJgK0rtIyIEubX4WH\n",
       "fWLSGn0A/mtTrHdV29IXl1n6vbYlopH8RyqpnNXWpG+1KhhNSCowxzGSOtrZmJMNxePHGP5TdtnR\n",
       "Q1MXjM4SlbIHNVtSaamz8y9z3dtPTRqld0C0dE/jDRwXz5sdPRcq5XJe1d0EyMKWDKy6vK5OcySg\n",
       "V3Yr9UI5X+MLmKndDZAE9FvhYT9bIBIM6UO/PXBhSxPClE7D99a2hF5U5zEBrLamIF665rclpLRb\n",
       "ZsqTgSmrjbnaleIDik+BuFdmeFNUxlzM0PmYWxuTan8vDnOQ/rosnGu+HoQM5gZ4u3RjQqnnA5C+\n",
       "P6WUvwebp52bcyW9MmQF3sKGVLEl3RpJ98+N+mq2oGjPDfLCunpGnljnSepYE2yreGdbkpLgozG/\n",
       "d+npakvaelefvzQb06ZERHQ1Twam2O/WbWxMU1/NxjTgLYsFYmxK85oGPlZn7Zq6r9qpNGn39VGT\n",
       "Rul1b8eeh2TzlP35ZYrEbcobNmRa2xpABBo1ts5HtpP+FZwMOKu8PaeAZS+xYRkEXJvjMhH1uCc8\n",
       "7n1KmF1EbKgSN1lgVshZEEgSyL8/4hUHljlHgFb18HuX98xfavpcqWOIkJKHVNliY9qSvDEsX1Fn\n",
       "MQqQxHh0WXonuWgkT2s8WmgUFO72vMZjrCzJzV1Atj3HmybKcm7PkN0xq6wroPQeC8AawJHtiHQf\n",
       "BhDoeGdL6rXYsKk2pmOWQYwo4yo8zqZ0vUofWu1Kf0QJtuSsi4eWbUu6VsTksHnvkvPdMX8J0Mob\n",
       "sjHdC4tGlbUbLIolo4OfefgvjRkzHjLHkQlkredYS0/OH6z4EzwBMDtARjMUAducc4GOqZCs7u5s\n",
       "x07lvB+QfRoWEHYsaZnTQLMDonA9KO7nd2puHbHu6A886gd++IdrvFL0hO64yQ/efsuHpcTz5eIS\n",
       "CyYg4a75S0eDq6NUHp4EmHH9GCO+QKDsyS8umwrspYukH/aBgZCKN2B2fd2ptl3Yykpp06XbGJCU\n",
       "v+ZjwIpke9HLvQDkmcBSAYmpooLTmgFgmcPcq6+XLGnXIMf9+UB5ON3P4y5gPvZHY1U4faSCCSQt\n",
       "w8MIh4ZWPH3Lh2xLq2GALwuuCDIbW94b85cu+ApCU1tDfZlfI6825s6WNMdOVV8dVJbPgDdKvMnn\n",
       "yodE/tTuuAOUG0CKty8NWpZe9kL5V0BSvhZ8cb7altWGBKrtiMyCaMC2WUAegKLGsuc80aycR7ou\n",
       "xVP9ST1N94uGlbbFc3jYb4kkZlPb0vAFEVLX4it2bIMm29KFhlhNyJYEinqqtuboOyI6aMRcJKIw\n",
       "A+y0GeOrcWm6ZNjPBpjNyaBYWXQCTMr5FUxbcImPQ7neqY27C5dilmuBpp0ozWSTwert6PkCfH5N\n",
       "AmSojj2DbaY9WpbbpRcggkBy9Z4k1vJgaazCgsqlES6xIuVLoL0ID/stkWXW29Q6AHVNrFqO3rmV\n",
       "LSOfFiiCQZ8O8QwkPGEb8jMgRk1fQU4n/fctOT1L+1yWV88NNkrp3Lyf24wIcIqOBXHJiAGKWDPa\n",
       "jKqiI1gCs2zAXEIVERsk4xggeVsAOfc9+3l+YosVnCsggxF7sK5qKqV385FY74U2LwGzAXhlSR+I\n",
       "Sl6rqLD6QG15KzyEKScshWzHmc7zlib3/gU20iarbTnLjVvEonSmQrh6auqeCT5naecvE2qzo8fV\n",
       "VhtutDBjyjEGxkGfkJShrBkfxpr3zeCMB0I4e+hpSpao94jjmvGO/l8Cy1Ae1PL5kD0SzpTegZEA\n",
       "nGxBlG/ohKoKrPG8FI8ByWUVUIHBVVk0A3s9n8sA5QtUIpVvlWbW9OtvhMfNUwLg0R9XtqWBFwpn\n",
       "rfRgtjVmI7DNxolXroBot6SuxpMloQGpujwqVDZkG5PnXNNIYro5I6cMDvEM+a2PsUsn4PFiAs0d\n",
       "H71+2qCC41ECW5zPwLN9kUVY29Z08fykvjbAcIBgF79Xdc3Yqc8bQIwKeXeaTJAMVWAvYCv39rTa\n",
       "eBfhqb/R86QhGp9pXryy/+n//EOqmAlH6PfeIOgavt9SA6V5KmrQ7lUeH7Wj06qT4a/+4vf2AnFS\n",
       "uXYPe5uhdNqZ0kNQzsIcvtE3fixfesXp7LfP/a//bnvOt6bMU9bzXN/+9aqVzbze3ja4aG/gr/7i\n",
       "d1ugno3Kmdq7mY/EKev5Kh9Xm/0lOTRRFZXf/xDpBuJOVu/AypcdlDyCMAhnGnwU+X//rz/0/BVY\n",
       "SHGU81G8dRL4VkWIKjC3WwvS2F75339/ERgTxgBeFlYXcBd8yYIvE/xsUzk4T9EyKrBD2Pl83f6P\n",
       "//jvLs97uU1d8/kVjPHM9hycHoPF6aAtbeblxT3/amnfOugRqC/6cd/PSADi/qqsWOWuyqSI4P/5\n",
       "u//ggiik0oLuAabri/DQZXbOgJ1tOTO65ueOHYgbgrE2Nj5ZycDUC9Zj3bszyHRI6LGlu7NHQK7h\n",
       "mU2dPuYwEld9BfyK1xiC+YOyI5bdAf7d23DaZMePjDpdUhxCuNZM7zl/hzwseabtt55nYHncztd0\n",
       "61eXVfHj+luTsHYtcS+n1SDEgZ/2FaDbLxI0zEhAnPXILJkGf69fVDrVGXHfe8LDFqQDJDiCZFsy\n",
       "sw3KKLB5yQlMixvI43zkdwDyqxTWVuZDIjtPQFMlnrfYhvb0vI6WGlj8nnxsnaCeZDUIw+mkB24j\n",
       "KuARZc2yb8Ftad3t6ftAmTNVMIfcSUrzqAmt31O8IKHrxM9Jul5kvV8GYQUjpRuYCFRJk6oVorrY\n",
       "9SkdBEiKo8aprTJDGmviicKQ2gtfwrB4Fl+EF+FFALAOfhy+rEz5ZcT7i/Ai/IsND/O+vggvwotw\n",
       "X3gByhfhRXjOwgtQvggvwnMWnitQfuQjH8E73/lOvOc978H3f//34+///u+f9SNdhl/5lV/Bu971\n",
       "Lrzuda/DH/3RHz3rx9mGz3zmM3jHO96Bt7/97fj4xz/+rB/nMvzoj/4o3vSmN+GbvumbnvWj3BVe\n",
       "eeUVfPu3fzve9a534d3vfjd+7ud+7rUXKs9R+M3f/E159dVXRUTkox/9qHz0ox99xk90Hf78z/9c\n",
       "/uIv/kK+7du+Tf7wD//wWT9OG/75n/9Z3vrWt8pf/uVfyhe/+EV5z3veI3/2Z3/2rB9rG37v935P\n",
       "/uiP/kje/e53P+tHuSv87d/+rfzxH/+xiIj8wz/8g7z88suvuX2fK6b8wAc+gENfRnz/+9+Pv/7r\n",
       "v37GT3Qd3vGOd+Dll19+1o9xGT772c/ibW97G97ylrfgK7/yK/GhD30In/rUp571Y23Dt37rt+Kr\n",
       "v/qrn/Vj3B2+5mu+Bu9973sBAG984xvxzne+E3/zN3/zmsp8rkDJ4ROf+AS++7u/+1k/xv/vwxe+\n",
       "8AV8/dd/vcdfeuklfOELX3iGT/QvN3z+85/HH//xH+P973//ayrnoSt6gC/NL3k9MtzzvM9zeLGA\n",
       "4zHhH//xH/GDP/iD+Nmf/Vm88Y1vfE1lPRyUX4pf8npkuPW8z3t485vfjFdeecXjr7zyCl566aVn\n",
       "+ET/8sI//dM/4Qd+4AfwIz/yI/i+7/u+11zec6W+2i95fepTn7r+Ja/nMMhzunrpfe97Hz73uc/h\n",
       "85//PL74xS/ik5/8JL73e7/3WT/Wv5ggIvjwhz+Mb/zGb8RP/uRPfskKfW7C2972NvmGb/gGee97\n",
       "3yvvfe975cd+7Mee9SNdhl/7tV+Tl156Sd7whjfIm970Jvmu7/quZ/1Ibfj0pz8tL7/8srz1rW+V\n",
       "j33sY8/6cS7Dhz70Ifnar/1aef3rXy8vvfSSfOITn3jWj3QZfv/3f1/GGPKe97zH5fY3fuM3XlOZ\n",
       "X9YF6S/Ci/AiPHl4rtTXF+FFeBFegPJFeBGeu/AClC/Ci/CchRegfBFehOcsvADli/AiPGfhBShf\n",
       "hBfhOQv/H/C06ftdL/8gAAAAAElFTkSuQmCC\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "#means\n",
    "mux=0\n",
    "muy=2\n",
    "#standard deviations\n",
    "sigx=1.5\n",
    "sigy=3\n",
    "\n",
    "#normal dist\n",
    "rvx = norm(loc=mux, scale=sigx)\n",
    "rvy = norm(loc=muy, scale=sigy)\n",
    "\n",
    "#peak occurs at (x,y)=(mux,muy), lets center image on that location\n",
    "numPoints = 100\n",
    "delX = 3*sigx/float(numPoints)\n",
    "xDomain = [mux - (delX)*(numPoints/2.0-i) for i in range(numPoints+1)]\n",
    "\n",
    "delY = 3*sigy/float(numPoints)\n",
    "yDomain = [muy - (delY)*(numPoints/2.0-i) for i in range(numPoints+1)]\n",
    "\n",
    "m = len(xDomain)\n",
    "n = len(yDomain)\n",
    "pdfData = numpy.zeros([m,n])\n",
    "\n",
    "for y in range(n):\n",
    "    for x in range(m):\n",
    "        pdfData[y][x] = rvx.pdf(xDomain[x])*rvy.pdf(yDomain[y])\n",
    "\n",
    "fig = pyplot.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "fig.subplots_adjust(top=1.5)\n",
    "ax.imshow(pdfData, extent=[min(xDomain), max(xDomain), min(yDomain), max(yDomain)],cmap=cm.coolwarm) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Bayes' Rule for Continuous Random Variables**\n",
    "\n",
    "Let *Y* be a continous RV:\n",
    "\n",
    "If *X* is also a continous RV, then\n",
    "\n",
    "$$f_{X\\vert Y}\\left(x\\vert y\\right) = \\frac{f_X\\left(x\\right)f_{Y\\vert X}\\left(y \\vert x\\right)}{f_Y\\left(y\\right)}\n",
    "=\\frac{f_X\\left(x\\right)f_{Y\\vert X}\\left(y \\vert x\\right)}{\\int_{-\\infty}^{\\infty}f_X\\left(t\\right)f_{Y\\vert X}\\left(y\\vert t\\right)dt}$$\n",
    "\n",
    "This formula has wide application and is commonly referred to as **inference**. It applies to situations where there is a RV *X* whose value we wish to obtain but cannot measure. It is further assumed that there is a related value *Y* that we can measure and that is related to *X*. If we can construct suitable models of the probability of *Y* given some value of *X* and a *prior* probability model of *X*, then we can infer the value of *X*, with some probability, given an observed value of *Y* using the above formula.\n",
    "\n",
    "If *N* is a *discrete* RV, then\n",
    "\n",
    "$$P\\left(N=n, \\vert Y=y\\right) = \\frac{p_N\\left(n\\right)f_{Y\\vert N}\\left(y\\vert n\\right)}{f_Y\\left(y\\right)}\n",
    "= \\frac{p_N\\left(n\\right)f_{Y\\vert N}\\left(y\\vert n\\right)}{\\sum_i p_N\\left(i\\right) f_{Y\\vert N}\\left(y\\vert i\\right)}$$\n",
    "\n",
    "$$f_{Y \\vert N}\\left(y\\vert n\\right) = \\frac{f_Y\\left(y\\right)P\\left(N=n\\vert Y=y\\right)}{P_N\\left(n\\right)}\n",
    "=\\frac{f_Y\\left(y\\right)P\\left(N=n\\vert Y=y\\right)}{\\int_{-\\infty}^{\\infty}f_Y\\left(t\\right)P\\left(N=n \\vert Y=t\\right)dt}$$\n",
    "\n",
    "**NOTE:** Be careful with the limits of integration. Often, the PDF of interest is zero outside some range $\\left[a,b\\right]\\hspace{1pt}$ in which case the limits of integration should be *a* and *b* respectively."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example**\n",
    "\n",
    "Assume the RV *Q* represents the probability of success for a Bernoulli RV X and has PDF\n",
    "\n",
    "$$f_Q\\left(q\\right) = \\left\\{ \\begin{eqnarray} 6q\\left(1-q\\right)&,& \\quad \\mbox{if} \\hspace{2pt} 0\\le q \\le 1 \\cr\n",
    "0 &,& \\quad \\mbox{otherwise} \\end{eqnarray} \\right.$$\n",
    "\n",
    "where $P\\left(X = 1 \\vert Q=q\\right)\\hspace{1pt}$. Using Bayes' Rule above, we can obtain\n",
    "\n",
    "$$f_{Q\\vert X} \\left(q \\vert x\\right) = \\frac{f_Q\\left(q\\right) p_{X\\vert Q} \\left(x \\vert q \\right) } {\\int_0^1 f_Q\\left(q\\right) p_{X\\vert Q} \\left(x \\vert q\\right) dq}$$\n",
    "\n",
    "which yields\n",
    "\n",
    "$$f_{Q\\vert X} \\left(q \\vert x\\right) = \\left\\{ \\begin{eqnarray} 12q\\left(1-q\\right)^2&,& \\quad x=0 \\cr\n",
    "12q^2\\left(1-q\\right)&,& \\quad x=1 \\end{eqnarray}\\right.$$ \n",
    "\n",
    "We wish to simulate this below. We will need to create random samples for *Q* that obey the distribution $f_Q\\hspace{1pt}$, then use the corresponding value *Q=q* to obtain a value for *X* by choosing a random value from a uniform distribution. If that value is less than or equal to *q* then that *X* will be considered a success. \n",
    "\n",
    "To obtain appropriate values of *Q*, i.e. those that obey it's distribution, we first compute the CDF of Q as\n",
    "\n",
    "$$F_Q\\left(q\\right) = \\int_0^q 6t \\left(1-t\\right)dt = 3q^2 - 2 q^3$$\n",
    "\n",
    "To obtain observations of *Q* we use inverse transform sampling, that is we choose a value, *y*, from a uniform random variable on *[0,1]* and find the value *q* satisfying $y=CDF\\left(q\\right)$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1087a06d0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAABCoAAAG1CAYAAAA/XRX7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xlc1XX2x/HXZROQRRBlEdydxN3c0jJxSi0rM9csy7Sy\n",
       "KTWXsalRS2zMlslsoXFsyvw1ZmZNiy1qMyZli1qWLWruLIqgKCLIdrnc3x9XL5CICBe+93Lfz8eD\n",
       "h3yX+73nC3jgnvv5nI/JarVaERERERERERFxAh5GByAiIiIiIiIico4KFSIiIiIiIiLiNFSoEBER\n",
       "ERERERGnoUKFiIiIiIiIiDgNFSpERERERERExGmoUCEiIiIiIiIiTkOFChEREalViYmJDBw40Ogw\n",
       "RETkApSnxdmoUCGGadmyJf7+/gQGBhIREcHEiRM5c+YMAHFxcfj5+REUFERwcDA9e/bk6aefpqio\n",
       "yP74+Ph4vL29CQwMtH88++yzF3y+FStW0LlzZxo2bEhkZCQPPPAA2dnZtX6fIiK1zZXzqcVioU+f\n",
       "PixatKjcvl69evHcc89V65oXsmbNGvr160fDhg31B7mI1Cnl6aopLCxk0qRJBAcHExkZyZIlSxx6\n",
       "fXEdKlSIYUwmEx9//DE5OTn88MMPfP/99yxcuNB+7OWXX+b06dOkp6ezePFiVq9ezdChQ8s9fty4\n",
       "ceTk5Ng/Zs+eXeFzLV68mEceeYTFixdz+vRptmzZQnJyMoMGDcJsNtfJ/YqI1BZXzqeenp4sX76c\n",
       "p59+mj179gDw7LPP4unpycyZM6vx1biwxo0bM2vWLB555BGHXldE5GKUp6smPj6eAwcOkJKSwqZN\n",
       "m3jmmWfYsGGDQ59DXIMKFeIUoqKiuO6669i5c6d9n9VqBcDPz48BAwawdu1avv32Wz755BP78XPn\n",
       "VOb06dPEx8eTkJDA4MGD8fT0pEWLFqxZs4akpCRWrlxZOzclImIAV8ynHTt2ZNasWdxzzz3s3r2b\n",
       "J598ktdeew2TyVSt613INddcw6hRo4iMjHTodUVELoXy9IW98cYbPProowQHB9O+fXsmT57MihUr\n",
       "HPoc4hpUqBBDnUu4qamprFu3ju7du9uP/T7xxcTE0LNnTzZv3nxJz/HNN99QUFDAiBEjyu1v2LAh\n",
       "Q4cO5X//+181oxcRcR6unk/nzJlDdnY2V199NTNnzqRjx44XPPepp54iJCSkwo/Q0NBqxyAiUpuU\n",
       "pyvP01lZWRw9epSuXbva93Xp0qVcQUfchwoVYhir1crw4cMJCQmhf//+xMXFMWfOnEofExUVRVZW\n",
       "ln17zZo15ZJeenr6eY/JzMwkLCwMD4/zf9wjIiLIzMys+c2IiBioPuRTb29vevfuzcmTJ7n99tsr\n",
       "PfeRRx4hKyurwo+TJ09WOwYRkdqiPH3xPJ2bmwtAcHCwfV9QUBA5OTnVjllclwoVYhiTycSHH35I\n",
       "VlYWSUlJJCQk0KBBg0ofc/jw4XJV2LFjx5ZLehEREec9JiwsjMzMTEpKSs47dvTo0QofIyLiSupD\n",
       "Pt28eTMffvghEyZM4MEHH6z2dUREnJHy9MUFBAQAtukr52RnZxMYGOjw5xLnp0KFuIzU1FR++OEH\n",
       "+vfvb99Xlbl6ffv2pUGDBvznP/8ptz83N5f169czePBgh8cqIuLMnC2f5ufnc/fdd7N48WISEhLY\n",
       "s2cPb7755gXPX7RoUbnO92U/goKCLvp8jp5TLSLiaO6Yp0NCQoiMjGTHjh32fT/99BOdOnWqVszi\n",
       "2lSoEKd1Lhnn5eXxxRdfcPPNN9OnT59yHZCrIjg4mPnz5zNt2jQ2bNiA2WwmKSmJMWPG0KZNG8aO\n",
       "HVsb4YuIOA1nz6fz58+ndevW3Hnnnfj7+7Ns2TJmzpzJiRMnKjx/zpw55Trfl/0o+07c75WUlFBQ\n",
       "UIDZbKakpITCwkKt/CQiTkF52ubOO+9k4cKFnDp1it27d/Pqq69y1113VStmcW0qVIjTmjp1KkFB\n",
       "QURERDBz5kxGjx7N+vXr7cdNJlOV3xV76KGHWLRoEbNnzyYoKIjWrVtjMplYv349Xl5etXULIiJO\n",
       "wZnz6ffff88rr7zCsmXL7PuuvfZabrzxRmbMmHHJ16vMG2+8gb+/Pw888ACbN2/Gz8+P++67z6HP\n",
       "ISJSHcrTNgsWLKBNmza0aNGCgQMH8vDDD2v0s5syWasyhkiknlmxYgUPP/ww3377La1btzY6HBER\n",
       "l1WVfJqYmMiCBQvYtGlTHUcnIiLK0+KKKh1RMWnSJMLDw+ncuXOFxzMzM7nuuuvo1q0bnTp10hq3\n",
       "4jLuuusuFi9ezNatW40ORaRGUlNTGThwIB07dqRTp068+OKL552TmJhIcHAw3bt3p3v37ixcuNCA\n",
       "SKW+Uj4VqZzytBhNeVpcUaVjfyZOnMi0adO48847KzyekJBA9+7defLJJ8nMzOSyyy5j/PjxGkov\n",
       "LmH8+PFGhyBSY97e3ixZsoRu3bqRm5tLjx49GDRoELGxseXOGzBgAGvXrjUoSqnvLpZPL2XIskh9\n",
       "ozwtzkB5WlxNpSMq+vfvT0hIyAWPR0ZG2puhnD59msaNG6tIISJShyIiIujWrRtgW9YrNjaWtLS0\n",
       "887TLD8x0oABA/j888+NDkPEEMrT4gqUp8XZ1KiqcO+99/LHP/6RqKgocnJyWLNmTYXnqTonIq7I\n",
       "1f5oTEpK4scff6RPnz7l9ptMJr755hu6du1Ks2bNePbZZ+nQocN554iIuBrlaRER51bdPF2jVT8W\n",
       "LVpEt27dSEtLY8eOHUyZMoWcnJwLBuguH/Pnzzc8hvp2zwMGD6B9z/a079meAYMH1Pv7dbYPd7tf\n",
       "q9W1/vAF2/roo0aN4oUXXiAgIKDcscsvv5zU1FR++uknpk2bxvDhwyu8htFfc/1M6551v7rfS/lw\n",
       "NcrT+rnW/br3/brjPddEjQoV33zzDaNHjwagTZs2tGrVij179tQoIJGKZJzMIGJqBBFTI8g4mWF0\n",
       "OCJOxWw2M3LkSMaPH1/hH7eBgYH4+/sDcP3112M2mzl58mRdhyki4raUp0VELk2NChXt27fnf//7\n",
       "HwAZGRns2bNHSz2KiNQhq9XK3XffTYcOHS64lnlGRoa9qr1t2zasViuhoaF1GaaIiNtSnhYRuXSV\n",
       "9qgYN24cX3zxBZmZmcTExLBgwQLMZjMA9913H3PmzGHixIl07dqVkpISnnnmGSVVIC4uzugQ6py7\n",
       "3bPuV5zF119/zcqVK+nSpQvdu3cHbNPyUlJSAFuufvfdd1m6dCleXl74+/uzevVqI0N2Cu74M+1u\n",
       "96z7FWehPF197vZzrfut/9zxnqvLZK3p5JGqPInJVOM5KuLeYnvFEjE1AoD0hHR2f7fb4IikvnO3\n",
       "vOVu9ysirs/d8pa73a+IuL6a5C2tJSriIKGhoWRlZRkdhlyikJAQzQMWcRPK065JeVrEvShXu57a\n",
       "yNMqVIg4SFZWlt7pcEFa7k3EfShPuyblaRH3olztemojT9eomaaIiIiIiIiIiCOpUCEiIiIiIiIi\n",
       "TkOFChERERERERFxGipUiIiIiIiIiIjTUKFCRIiPj+eOO+4wOowKvfnmmwwZMqTG1/Hw8ODgwYMO\n",
       "iEhEpO4pT4uIOD/lasdRoULEDQQEBBAYGEhgYCAeHh74+/vbt1etWuU0HdWTkpLw8PCgpKTEvu/2\n",
       "229nw4YNBkYlIlL7lKdFRJyfcnXdUaFCxA3k5uaSk5NDTk4OLVq04OOPP7Zv33bbbXW2BFRxcXGV\n",
       "ztOSVCLibpSnRUScn3J13VGhQqSumEyO/XBoaCaKioqYMGECQUFBdOrUie3bt9uPp6WlMXLkSJo2\n",
       "bUrr1q156aWX7McKCwuZMWMGzZo1o1mzZsycOZOioiIAEhMTiY6O5plnniEyMpK7774bq9XKU089\n",
       "Rdu2bQkLC2Ps2LFkZWUBcPXVVwPQqFEjgoKC2LJlCytWrKB///7259u5cyeDBg2icePGRERE8OST\n",
       "TwKwbds2+vbtS0hICFFRUUybNg2z2ezQr5OI1HPK08rTIuLcnDhP28JTrnYUFSpEBKvVytq1axk3\n",
       "bhzZ2dkMGzaMqVOnAlBSUsJNN91E9+7dSUtLY+PGjTz//PN89tlnADzxxBNs27aNn376iZ9++olt\n",
       "27axcOFC+7UzMjLIysoiJSWFZcuW8eKLL7J27Vq+/PJLjh49SkhICFOmTAFg8+bNAGRnZ3P69Gmu\n",
       "uOKKcnHm5ORw7bXXMnToUI4ePcr+/fu55pprAPDy8uKFF17gxIkTfPvtt2zcuJF//OMftf61ExGp\n",
       "C8rTIiLOT7nagax1oI6eRuqx9j3bW+NWxFnjVsRZ2/dsb3Q4Fbrozzk49qOaWrZsad24cWO5ffPn\n",
       "z7cOGjTIvr1z506rn5+f1Wq1Wrds2WJt3rx5ufMXLVpknThxotVqtVpbt25tXbdunf3Yhg0brC1b\n",
       "trRarVbrpk2brD4+PtbCwkL78djY2HLPn5aWZvX29rZaLBbroUOHrCaTyWqxWOzHX3/9detVV11l\n",
       "tVqt1lWrVlkvv/zyKt3nkiVLrLfccot922QyWQ8cOHDeeRf6vrlb3nK3+xX3pDxtozztmtztfsV9\n",
       "Vfqz7iR52mpVri6rNvK0V92XRkTclJPPEQsPD7d/7u/vT0FBASUlJSQnJ5OWlkZISIj9uMVisQ8p\n",
       "O3r0KC1atLAfa968OWlpafbtJk2a4OPjY99OSkrilltuwcOjdECXl5cXGRkZF40xNTWV1q1bV3hs\n",
       "7969zJo1i+3bt5OXl0dxcTE9e/aswp2LiJylPA0oT4uIE3PyPA3K1Y6iqR8iUmmH4piYGFq1akVW\n",
       "Vpb94/Tp03z88ccAREVFkZSUZD8/JSWFqKioC167efPmrF+/vtz18vLyiIyMvGin5ObNm19wOaT7\n",
       "77+fDh06sH//frKzs3niiSfKdToWEXFlytMiIs5PudpxVKgQkUo7Avfu3ZvAwECeeeYZ8vPzsVgs\n",
       "/Prrr3z//fcAjBs3joULF5KZmUlmZiaPP/54petH/+lPf2LOnDmkpKQAcPz4cdauXQvYKsUeHh4c\n",
       "OHCgwsfecMMNHD16lBdeeIHCwkJycnLYtm0bYOvCHBgYiL+/P7/99htLly6t1tdCRMQZKU+LiDg/\n",
       "5WrHUaFCRDCZTOdVXs9te3p68vHHH7Njxw5at25NkyZNmDx5MqdPnwZg3rx59OzZky5dutClSxd6\n",
       "9uzJvHnzzrvOOdOnT2fYsGEMHjyYoKAg+vbta0+M/v7+zJ07lyuvvJLQ0FC2bt1aLrbAwED++9//\n",
       "8tFHHxEZGckf/vAHEhMTAXj22WdZtWoVQUFBTJ48mVtvvbXcczvLutYiItWhPC0i4vyUqx3HZK2s\n",
       "7OOoJzGZXHoNVzFebK9YIqZGAJCekM7u73YbHNH59HPumi70fXO376e73a+4J/2cuyblaRt3u19x\n",
       "X/pZdz21kac1okJEREREREREnIYKFSIiIiIiIiLiNFSoEBERERERERGnoUKFiIiIiIiIiDgNL6MD\n",
       "EIkbEkfGyQwAwkPDSdyQaGxAIiIiIiIiYhgVKsRwGSczyq3oISIiIiIiIu5LUz9ERERERERExGmo\n",
       "UCEiIiIiIiIiTkNTP0RqUdn+G7XBkT094uPjOXDgAP/+978dcr26sGLFCl577TU2b95sdCgi4qKU\n",
       "p2uX8rSI1JQr5WlQrnYUFSpEalHZ/hu14VJ7eqxYsYLFixdz8OBBgoKCuOWWW3jyyScJDg7GZDLV\n",
       "UpQiIs5LeVpExLk5W54G5eq6oKkfIm5i8eLFPPLIIyxevJjTp0+zZcsWkpOTGTRoEGazGavVWusx\n",
       "FBcX1/pziIi4KuVpERHnp1xdN1SoEKmCuCFxxPaKJbZXLHFD4owO55KdPn2a+Ph4EhISGDx4MJ6e\n",
       "nrRo0YI1a9aQlJTEypUrMZlMFBQUcOuttxIUFESPHj34+eef7dd4+umniY6OJigoiPbt2/P5558D\n",
       "YLVaeeqpp2jbti1hYWGMHTuWrKwsAJKSkvDw8GD58uW0aNGCa665hqFDh/Lyyy+Xi69r16588MEH\n",
       "APz2228MGjSIxo0b0759e9555x37eSdOnGDYsGEEBwfTp08fDhw4UNtfOhGROqE8LSLi/JSr644K\n",
       "FSJVcG7IWcTUiFqdI1dbvvnmGwoKChgxYkS5/Q0bNmTo0KH897//BeDDDz9kzJgxZGVlcdtttzF8\n",
       "+HAsFgt79uzh5Zdf5vvvv+f06dN89tlntGzZEoAXX3yRtWvX8uWXX3L06FFCQkKYMmVKuef58ssv\n",
       "+e2339iwYQPjxo3jrbfesh/btWsXKSkp3HDDDZw5c4ZBgwYxfvx4jh8/zurVq3nggQfYvXs3AFOm\n",
       "TMHf35/09HSWL1/O66+/ruF1IlIvKE+LiDg/5eq6o0KFiBvIzMwkLCwMD4/z/8tHRkaSmZkJQM+e\n",
       "PRkxYgSenp7MmjWLgoICtmzZgqenJ4WFhezcuROz2Uzz5s1p3bo1AMuWLWPhwoVERUXh7e3N/Pnz\n",
       "effddykpKbE/R3x8PH5+fvj6+jJ8+HB27NhBamoqAG+++SYjR47E29ubjz/+mFatWjFhwgQ8PDzo\n",
       "1q0bI0aM4J133sFisfDee+/x+OOP4+fnR8eOHZkwYUKdDK8TEaltytMiIs5PubruqFAh4gbCwsLI\n",
       "zMwsl+jOSUtLIywsDIDo6Gj7fpPJRHR0NGlpabRt25bnn3+e+Ph4wsPDGTduHEePHgVsQ9FuueUW\n",
       "QkJCCAkJoUOHDnh5eZGRUTryJCYmxv55YGAgN9xwg70CvHr1am6//XYAkpOT2bp1q/1aISEhrFq1\n",
       "ioyMDDIzMykuLi53rebNmzvwqyQiYhzlaRER56dcXXdUqBBxA3379qVBgwb85z//Kbc/NzeX9evX\n",
       "c+211wLYK7IAJSUlHD58mKioKADGjRvH5s2bSU5OxmQy8fDDDwO2xLZ+/XqysrLsH3l5eURGRtqv\n",
       "9fuhZOeGqn377bcUFBQwcOBA+7UGDBhQ7lo5OTm8/PLLhIWF4eXlRUpKiv06ZT8XEXFlytMiIs5P\n",
       "ubruqFAh4gaCg4OZP38+06ZNY8OGDZjNZpKSkhgzZgwxMTGMHz8eq9XK9u3bef/99ykuLub555/H\n",
       "19eXK664gr179/L5559TWFhIgwYN8PX1xdPTE4A//elPzJkzx57gjh8/ztq1ayuNZ+jQoSQnJzN/\n",
       "/nxuvfVW+/4bb7yRvXv3snLlSsxmM2azme+++47ffvsNT09PRowYQXx8PPn5+ezatYv/+7//c7r5\n",
       "dCIi1aE8LSLi/JSr646X0QGI1GfhoeHVWpv5Uq5fVQ899BCNGzdm9uzZHDhwwL7m81tvvYWPjw8m\n",
       "k4nhw4fz9ttvM2HCBNq1a8d7771nn0v317/+ld27d+Pt7c2VV17JK6+8AsD06dOxWq0MHjyYtLQ0\n",
       "mjZtyq233sqwYcOA8yu/AD4+PowYMYLXX3+dJ5980r4/ICCAzz77jFmzZjFr1ixKSkro1q0bzz33\n",
       "HAAJCQlMnDiRiIgIYmNjmTRpEomJiTX4CoqIu1OeVp4WEefmTHkalKvrislaSdeMSZMm8cknn9C0\n",
       "aVN++eWXCs9JTExk5syZmM1mwsLCKrxBk8nkdM05xHnE9oolYmoEAOkJ6ez+bne1zjE6Rv2cu6YL\n",
       "fd/c7fvpbvcr7kk/565JedrG3e5X3Jd+1l1PbeTpSqd+TJw4kfXr11/w+KlTp5gyZQofffQRv/76\n",
       "K++++261ghARERERERERgYsUKvr3709ISMgFj69atYqRI0fau5qe63IqIiIiIiIiIlIdNepRsW/f\n",
       "PsxmMwMHDiQnJ4fp06dzxx13VHhufHy8/fO4uDji4uJq8tQiTickJMTpmtDIxZ0rxiYmJjrd3DwR\n",
       "cSzladdU2ZtmIlL/KFe7ntrI0zUqVJjNZn744Qc2btxIXl4effv25YorrqBdu3bnnVu2UCFSH508\n",
       "edLoEKQGfl9AXbBggXHBiEitUJ4WEXF+ytUCNSxUxMTEEBYWhp+fH35+flx99dX89NNPFRYqRERE\n",
       "REREREQuptIeFRdz880389VXX2GxWMjLy2Pr1q106NDBUbGJiIiI1Iq4IXHE9oolbkic0aGIiIjI\n",
       "71Q6omLcuHF88cUXZGZmEhMTw4IFCzCbzQDcd999tG/fnuuuu44uXbrg4eHBvffeq0KFiIiIOL2M\n",
       "kxlETI0gPSHd6FBERETkdyotVLz11lsXvcDs2bOZPXu2wwISEREREREREfdVox4VIs4kbkgcGScz\n",
       "AAgPDSdxQ6KxAYmIiIiIiMglU6FC6o1zw3gBDeUVERERERFxUSpUiNMqO0IiOTWZCCIMjkhERERE\n",
       "RERqW41W/RCpTedGSERMjcBisRgdjoiIiIiIiNQBjagQt6feFiIiIiIiIs5DhQpxe+ptISIiIiIi\n",
       "4jw09UNEREREREREnIYKFSIiIiIiIiLiNFSoEBERERERERGnoUKFiIiIiIiIiDgNFSpERERERERE\n",
       "xGlo1Q9xaWWXFk1OTSaCCIMjEhERERERkZrQiApxaeeWFo2YGoHFYjE6HBEREREREakhjaiQeik5\n",
       "KZnYXrEAhIeGk7ghsdzoi3P7RERERERExLmoUCH1kgULEVNt00DSE9KB0tEXZfeJiIiIiIiIc1Gh\n",
       "QlxOclIysT3b0ycnj7+mpOH5Th4fDYwyOiwRERERERFxABUqxKV4m0sYX1DEwxmHaXP4jG3nJync\n",
       "+mkKH3qb2LQ3m1/bBRkbpIiIiIhIHdH0ZqmPVKgQlxBRYuWu9w4xbFMaIbkWyD1T7rinFUYUWRmx\n",
       "6Ef2tAzkyQILR4pLKPZSv1gRERERqb80vVnqIxUqxBBVXVa0XVIOIz87zMCTZnzWJpc7lu/jwb89\n",
       "oHubYHrtzLLvvywphxXAiT9v4YNrmvGa2bO2bkNEREREREQcTIUKMUTZyu/B2QfLH7RY4MMPeeO3\n",
       "ZHp9n3/eY5M94NPRbfj06gg+m/8d/R7qSsvDZ7jyb9u5owQamEsAaJxdxN3vHWK8yQT33EO7vAJy\n",
       "av3ORERERMTdaTqGSM2oUCEVqkpydXQCbphXzIT0k9C2LSQl0et3x39pF8y7g6P5++q99Lk+ptyx\n",
       "pOiGrAr04qP5vbgpMY2h7x8iylavoIHVCq+9xlpg+zPZvDs4mg+t1hrFejH65SQiIiLivjQdQ6Rm\n",
       "VKiQClUluToqAbexWJm6ch/Xf5WOf4Gl3LFiTxObejdl/q4TNJjbHQDL2/sueK3Tgd68eVMLZiQe\n",
       "5pFRbRn12WHaHyodR9FjVxY9dmVxXwNvSEiAu+6qdtyV0S8nERERERGR6lGnQTGG1Ur3XVksfP4X\n",
       "fs0yM/J/R8oXKRo3ZmlkY8Y9ewWL7otlu/el/aiaTSY29g3n/scu57b2zWH0aMqWQFoWmmHaNIiO\n",
       "5qHUY4RnFjjmvkRERERERKRGNKJC6lZBAaxaxQe7krhse+F5h/f5+tDupZfh9tt58erLiQhpULPn\n",
       "M5n4McAf1qxhcJe23BNdxE1fHCUgr9h2PDubSdkw4aEtfNWjCa/k+IHVCiZTzZ5XREREREREqkWF\n",
       "CjdXZ70Ujh6FpUttH5mZXPa7w992bcy7g6P59PMCdt9zT62EkNbAm1fGxvDGzS3pu2gvj/kGw969\n",
       "gG150wHfH2cAQK9eMGMGjBkDPj41ft7kpGRie8UC6lchIiIiIiJyMZr64ebO9VKImBphL1g41Pbt\n",
       "cOed0KIF/O1vkJlpP5Tv48H71zSjUyNv5szszA8dQ+pkJEOBrydvNQ2B3bvhk0/4Osj//JjvuMMW\n",
       "88KFcPx4jZ7PgqV2v8YiIiIiIiL1iAoVcknihsQR2yuW2F6xJKcmV3jOHwcPYFrbaL4L9IeePeHf\n",
       "/wazufSE5s15JroJY5b05cU72rHPy6BpFh4eMHQo9/yhORMX9uKjAZEUlC2UpKfDo49CTAx/SzpK\n",
       "q9RcY+IUqURqaioDBw6kY8eOdOrUiRdffLHC8x588EHatWtH165d+fHHH+s4ShER96U8LSJy6TT1\n",
       "Qy5J2dUsDs4+WP7gqVPw2mu88cW3RBeZz3/wlVfaplQMH87rfTsT0dC7DiKumqTohjw38TIWnWrI\n",
       "t2Mm2lYEOXrUdrCwkFGFhYx69Hu2dwjh1SJ/KCmxFTpEDObt7c2SJUvo1q0bubm59OjRg0GDBhEb\n",
       "G2s/59NPP2X//v3s27ePrVu3cv/997NlyxYDoxZxflpmWhxFeVpE5NLplZbUWFCumbkpGRAdDbNn\n",
       "lytSmE3A7bfDtm3w1VcwahR4OW997JS3F8yZA0lJ8OabthEhZfTYlcXS/UfgssvglVdsjTdFDBQR\n",
       "EUG3bt0ACAgIIDY2lrS0tHLnrF27lgkTJgDQp08fTp06RUaGpiGJVKbWp0aK21CeFhG5dM77ilFc\n",
       "QoNCC4uf3kHbY2fK7c8O8GbtwCj+lezFlytXGhTdpTuv8eW2bfDtt6y78ToGn8rB81xdYv9+uO8+\n",
       "SEmx9bEQcQJJSUn8+OOP9OnTp9z+I0eOEBMTY9+Ojo7m8OHDhIeHlzsvPj7e/nlcXBxxcXG1Ga6I\n",
       "yCVJTEwkMTHR6DBqRHlaROozR+ZpFSqkRh5cuY+2qWWKFB07Mi/3BN/NbUeRjyfHE9KNC64azjW+\n",
       "BEhPSLc19+zXj1ltmtH11kbcvPEIN3x2hCBLie0BTzxhm9Jy/fUGRi0Cubm5jBo1ihdeeIGAgIDz\n",
       "jlt/N/rHVEHj2rJ/AIu4C63M5Dp+/8J8wYIFxgVTDcrTIlLfOTJPa+qHVNudBRaGbi5TiHj+efjl\n",
       "F/7TpBFFPp7GBVZLMsJ8eWVsGwZ2aQvXXmvff+qmG/ljl7bEDYkzLjhxa2azmZEjRzJ+/HiGDx9+\n",
       "3vFmzZqRmppq3z58+DDNmjWryxBFnJZWZpK6oDwtInJpVKiQammdmsuLuRb79oehQfDgg3WyvKjR\n",
       "8jw9bP0roqIAaGQpISHvOCczXWv0iNQPVquVu+++mw4dOjBjxowKzxk2bBhvvPEGAFu2bKFRo0bn\n",
       "DScWEZHaoTwtInLpNPVD7MoOf01OTSaCiArP888vJj5hJ35ntw9F+XN3YRGP9O5Q6WPLdlCv7Pou\n",
       "oWlTePuWvSppAAAgAElEQVRtivv3xwvocOA0f25a/0aRiPP7+uuvWblyJV26dKF79+4ALFq0iJSU\n",
       "FADuu+8+hg4dyqeffkrbtm1p2LAhr7/+upEhi9QKrdIhzkp5WkTk0qlQIXZl+zOct/ToOVYrs5fv\n",
       "ISYjH4D8Bp7ET+1IznM/0fkij610aVNXdNVVPBfdhL8cPg7AhGNZ8O67tpVNROrIVVddRUlJyUXP\n",
       "S0hIqINoRIxT9ndMuov1R5L6TXlaROTSVTr1Y9KkSYSHh9O5c+dKL/Ldd9/h5eXFe++959DgxPnc\n",
       "fiyLgd8dt28vvusPpEQ1dNj1z43qiO0VS3JqssOuW1vP83p4KF9dHmbfzh07lus6t6nV2EVERERE\n",
       "ROqzSgsVEydOZP369ZVewGKx8PDDD3Pddded161Y6pmtW/nL4WP2zWW+Hmzs69j5k2Wbmlkslos/\n",
       "wOjnMZl46p72pDXxBSCgpISE7Ay8i4sdFKmIiIiIiIh7qbRQ0b9/f0JCQiq9wEsvvcSoUaNo0qSJ\n",
       "QwMTJ3PiBIwejc/ZWtSeFgE81FA9GQDO+HuxYEpHCs9ut009w/O5tVdkERER9xI3JM4+ClArTImI\n",
       "iDuoUY+KI0eO8OGHH/L555/z3XffVbje8zll133+/fqq4txMVivccQecXTYrx9+L+KkdKXz6R4Mj\n",
       "cx57WwYyq6EnL5+xFSgmFpaQ8VU6G65y4YahbiYxMZHExESjwxAROY/6b4g4r7KNfI8ePkpkdCRQ\n",
       "DxrHixisRoWKGTNm8NRTT2EymbBarZVO/ShbqBDXcm/6Cdi+x7791L3tSW/iV8kj3NOrvh4M7xLG\n",
       "oG9tv6xmvLGXvS0C+MbguKRqfl9AXbBggXHBiIiIiEv4fbP4etU4XsRANSpUbN++nVtvvRWAzMxM\n",
       "1q1bh7e3N8OGDXNIcGK8bruzePBIpn371fBQvukeVskj3JjJxHMT/kC75BxapuXhW1RC/Ms7WVui\n",
       "3i0iIiIiIiJVVWmPios5ePAghw4d4tChQ4waNYqlS5eqSFGPhJ4q5NF/7sbeieKqq3ihmXqRVKbA\n",
       "15P4KR05c3a7eXo+S3MtoEazIiIiIiIiVVJpoWLcuHH069ePPXv2EBMTw/Lly1m2bBnLli2rq/jE\n",
       "IJ5WK4/+czeh2UW2HU2awOrVFHtcuA+J2CQ3a8gDAaWNRkcXlTB8Y5qBEYmIiIiIiLiOSqd+vPXW\n",
       "W1W+0Ouvv17jYMR5zM+z0O23UwCUAB6rVkGzZsYG5UJW+3oyslc4wzbZChQPvLWf31oHohZoIiIi\n",
       "IiIilavR1A+pn/r8dIKH80vs2wlRYXDttQZGVDPJScnE9oolOTW5Tp834ba27GkRAIC3xcr8f+wi\n",
       "uLh02VItNyciIiIiInI+FSqknPDMAua8stu+/V2nEP4Z2djAiGrOgoWIqRFYLJaLn+xAZm8PFkzp\n",
       "yKmzs2UiMgt46lAalNiKQOe6REdMjbAvayUiIiIiIuLuVKgQO2+rlcf+sZOgM8UAHA9pwBOTY7Ga\n",
       "1Jeiuo429eOegNIZVnHZZ+CZZwyMSERERERExLmpUCF2T5+x0OFgDgBmYMEDHcgO8jE2qHrgowYe\n",
       "vH1dTOmOuXPhiy+MC0hERERERMSJqVAhAAzYdowpBaV9KeY09GRnu2ADI6pf/jWqFb+c+3qWlMCt\n",
       "txJmLjY2KBERERERESekQoUQnZ7HQ8v32Le/7BHGi7760XAki5cHjz/QgRNeZ5ctTU/n7wfT8Cix\n",
       "GhuYiIiIiIiIk9GrUTfnaykhPmEnDQtsjSaPNPXjmbvbg/pSOFxmSAMeah1l/9pekZPHXe8nGRuU\n",
       "iIgYQis/iYiIXJjXxU+R+mxeSgZtTpwBoACYP7UjZ/z1Y1FbVp/MpHtkY6alZQJwx0fJ/NouiLUG\n",
       "xyUiInXr3MpPAOkJ6QZHIyJGiBsSZ1/5LTw0nMQNicYGJOJENKLCnS1fzsgT2fbNmQGeHGgeYGBA\n",
       "9Z8FCx8s7Mh3HUPs++Ys201kodnAqERERESkrmmpepEL01vnbihuSByNDiezencyvmf3begXzvI9\n",
       "J+lXwfnJScnE9oq1fZ6aTAQRdRarkWrrvks8TDxxXywJM74hugSCzxTz3MEjUFQEPlplRUTEmekd\n",
       "UBERkdqnERVuKPd4Gi+dyMDXamvkeKhZQ56f8IcL9qWwYLFXey0WS12GaqjavO/sIB/GB3ph8bB9\n",
       "zbudKYCHHnLoc4iIiOPpHVAREZHap0KFu7FaWZiUTkxGPgC5QPyUDhQ08DQ2Ljf0rbcHy8a0Lt3x\n",
       "4ovwzjvGBSQiIiIiIuIEVKhwNy+9xHVZOfbN+wM9SYlqaGBA7u2dIdFsvjysdMfdd8PevcYFJCIi\n",
       "IiIiYjAVKtzJ1q0we7Z984M/RrFGIymMZTLx9D3tSWngbdvOyYHRoyE/39i4REREREREDKJCRT1z\n",
       "wXXZT5ywvQA221aX2NMykH+Ma2tMkFLOGX8vZrRuBg0a2Hb8/DNMnWpsUCIiIiIu7IJ/E4uIS1Ch\n",
       "op6psMlXSQnccQekpgKQ7elB/JQOmL317XcWuxv6wgsvlO5YvhxWrDAsHhERERFXpsa3Iq5Nr1Td\n",
       "wVNPwbp19s2/tookvYmfgQFJhSZPhvHjS7cfeAB++cW4eERERERERAygQkV9t2kTPPpo6fZf/sKm\n",
       "RoHGxSMXZjLBP/8JHTrYtvPzYdQoOH3a2LhEREREnJSmeIjUTypU1GNhRcUwbpxt6gdA//7wxBPG\n",
       "BlUPJCcl238hJqcmO/aacT25s5E/NDy7EsvevXDvvWC1OuR5REREROoTTfEQqZ+8jA5AaoeHxcri\n",
       "Q2mQk2fb0bQprF4NXvqW15QFCxFTIwA4OPugw6/5XUI6vPIK3H677eCaNbYikxpsiogTixsSZ3+R\n",
       "EB4aTuKGRGMDcmP6XoiIiKvTq9Z6auL7h+h9rkhhMsGqVRAVZWxQUnW33QabN9umggDMmgW9e9s+\n",
       "RESc0Ll3NQHSE9INjsa96XshUn0q9Ik4B039qIf6/HSC8R+nlO5YsACuuca4gKR6liyByy+3fW42\n",
       "w5gxcPKksTGJiEjlzGbIyTE6ChGppoyTGbS6O4zoPzXVVBIRA2lERT0TVWhmziv7S3cMGQJz5xoX\n",
       "kFSfry+8846tWJGdDcnJcOedsHYteKjGKCLuw1HvcJa9TnJqMhFE1CiuhhaLbfTbjh3w44+2f3fu\n",
       "hKIiW0+oOXNqdH0RqXt3Hz3BrAd+w+JhYp+PD0yaBN262T66doXgYKNDFHELKlTUJ4WFLDlwhKC8\n",
       "YgCOensRuXKlXtS6stat4f/+D4YPt21/8gk8/TT89a/GxiUiUoccNZWh7HUuqceQ1QpHjsCOHfwp\n",
       "LZNuCSdom5JLs2P5cPXVFT9m7lxo0aK035CIOL+33mL2keOArd9bh/xCeP318ue0bm0rWnTvDt26\n",
       "EV5ktuUIk6lKT1GTgqmmpYg7UaGiPnn4YbrkFQBQ7GliZptmrA4LMzgoqbGbb4bZs+HZZ23b8+bB\n",
       "lVde+I9jERGpPosF9u7lhhPZ9Hj7DG1Tcmm95zRERwMwHSCtite6+27bi5q+fWsrWhFxlK1bYeLE\n",
       "i5938KDt4733AEgETj2Ywv7mAXxxppj8bzPY3zyALRdYsa3aBVPUf0bciwoV9cWBA/DSS/bNZWNa\n",
       "89M+bwMDsjm37CY4Zpit21q0CLZsga++si03O3u27RdqFav3IiJyvgaFFnqZS7hpUxptU3Jpsfsk\n",
       "BAZCfj7PAhyq/PFmE3h36Vo6LLx7d2jVCq6/HnbtgsJC24i4bdtsoytExDmlptr+rxYWApAc6c/D\n",
       "f+6C97/S+Pf9s0qnd+3cCcXF5z28UY6Znjuz6AmwbDcA/wCSHt/OgeYBbD9WYvs7rnPnursnERen\n",
       "QkV98dxzthewwPYOIbw7OBr2Gd8AqDaW8nRL3t7w1lvQtq3tl+h338GXX8KAAUZHJiLiGo4fp1/2\n",
       "GXp/mkKblFyis4po96fNeFqB/9t78ccHBkK3bvx7z68cvbEp+1oEsPXDHH7evuP8cz/6yLZK04kT\n",
       "cOwYDBsGX38NAQEOvy0RqaEzZ2z/R9NtIxROeXowZ0ZnMsJ8SQ/0h+nTS88tLLQVIXfssBcvcr/+\n",
       "moCzf4OX5Q90OJhDh4M53AS2kVUeHnzs40XS0pPsbx6Af1EJPqeLOBXkUye3KuJKVKioDzIzy82f\n",
       "e/PG5nqnvT6KjoYJE+CVVwBIvPkG7m8XozmKIiIV+eEH29Dsc00u09J4DWBfFR7brBmJuadIvTqM\n",
       "fS0C2JKYz2c/7QMPDxb1iiXialsB3uxxpuLHt25te+5rr7WtAvLzz7ZeFe+/r75RIs6kpATuuMOW\n",
       "IwC8vHiwTRRp4X4Vn9+ggW3kVPfu9l29e7an29hGtE3Jxfe13cRdFkK75FyaZBVW+HxtCopos/UY\n",
       "12w9xn0AD35DZiMfdlq9bb1tRoyAHj0cfqsirka/LeuDl1+G/HwAdvo34MfYRgYHJLXmz3+2F6Hi\n",
       "ss/Q55ZALZ0lIvI71588DT172lbe+PRTSKu4qYTFBLs94X9XNGXZmNZMahcDGRlw+DD3t4th+chW\n",
       "bO7ZhFRfn0svMFx9Nfzzn6Xba9dqFRARZ/Poo7YC4jlLl/JdoP8lXcJqMnG0qR+bezZhQUMv5s7o\n",
       "zJglfWkW6s2fH+rKP8e05qPQIIiNvWAeCTtVxIDsM7apvr16wcqVNbkrkXpBIypcXV4eJCTYN1+L\n",
       "aKzRFPVIhd2db74ZPvgAgDHrU9mKClMi4j7K9j6qaERZ7IHTPHnoqK0Lf1l+fuzwsJLSO5R9zQN4\n",
       "/4ODBDzTl01zt9LvTx0ASD+YDk2bOiwWJk2C3btLmyE//bTtxcqECRVeTx39RerQypW2wsA5M2fC\n",
       "PffAssUOuXymh4kfOobwQ8cQ0g/6cNN3uyAvjzE9O9CndwPapuQSvvko3TxM+BaVmTpitdoa8bZp\n",
       "o0a84tZUqHB1K1bYpn4AtGzJZyENaGJoQOJIFXZ3fughe6Fi0DcZNOnY0KjwRETqXNneR7/vet/k\n",
       "RAF/e/FXGpwrUrRvD489Zmt0+Yc/MO6KTkRMsD32u0+S6NfAs9ZisXvqKfjtN/j4Y9v25Mm2fkMV\n",
       "UEd/kQurSSHvvKJi/JO2YsBZ34aFcs+Xn1LSa13tNn/39+eXhn4cH2i7/je/ZHLVM31plpFP2L8O\n",
       "85xvI1sPjKIiNeIVt6epH67MYrE10Txn5kwsGk1R//Xrxw8NbXMnvS1W7jyWZXBAIiLG87OU8MQL\n",
       "v9I4u8i2IzTUVhwYN842isGzZkWJavP0hFWroFMn23ZREdxyC1GFZmPiEXFR5wp5EVMjLnna67mi\n",
       "YsTUCDyPHrYVAYrO5ooOHZgW05im0yKJmBqBxWKphegvrMTDRGqkP+tCg2w5KyzMduDYMbjpJsjJ\n",
       "qdN4RJyFChWu7P33bcuSAoSE2IaYiltYHhFq/3zs8VNw+rSB0YiIGKykhKcPpdEuJRewLRvKf/5j\n",
       "GzrtDAIDbSuBNDk75vH4cZbuP4xf/vnLHIpI7fEtsPDy/sO2IgBA48bw0UecMaqQ+XutWtn+vvf2\n",
       "tm3/8guMH297c1LEzahQ4aqsVvj730u3H3hAy565kc8bBZASYRtVEWgpgX/9y+CIREQM9OijDDqV\n",
       "a99c0DwC4uKMi6ciLVvaXoD42JYh/EN+IfOW7cajxFr540TEIUwlVuYt20X7fNtqHEUmGGotIHbs\n",
       "DSSnJhscXRlXXWVf4Q1wSCPeuCFxxPaKJbZXLHFD4moWn0gdUaHCVW3ebJu3BralkqZNMzYeqVNW\n",
       "k4l3rosp3fH887Yl8ERE3M3vGuKtGRLNf5o4aZPhK68sV1jut+ME975z0MCARNzHPf85xJU/nrBv\n",
       "Pz/xMjZ6mA2Z7nFRd91l60l2zjPP2PrSVVNNps2IGOWihYpJkyYRHh5O586dKzz+5ptv0rVrV7p0\n",
       "6cKVV17Jzz//7PAgpQJlR1PceSeEhxsXixhiw5URnAw6OzTw8GFYvdrYgERE6ljX3PxyDfG2dAll\n",
       "2Vgnme5xIXfeCQ8/bN+8dV0qIzJPGRiQSP03vsDCbZ+k2LdXXx/DuqsjDYyoCp580taj4pzJk7k8\n",
       "J8+4eETq2EULFRMnTmT9+vUXPN66dWu+/PJLfv75Zx599FEmT57s0AClArt2lXYPN5ngz382Nh4x\n",
       "hNnbg/evjbZv77nvXuIGDzAwIhGRuhOeWUDC/sP2hnj7fH342/0dKPFwgabSixbxv0al0zXnJ6fD\n",
       "l18aGJBI/dVpbzZLc0tHTHziY+Jfo1sbGFEVeXrCm29yIODs6m5mM8/vTSHieH6dhqFpI2KUixYq\n",
       "+vfvT0hIyAWP9+3bl+DgYAD69OnD4cOHHRedVGxxmfWdhw2Dyy4zLhYx1No/RnHm7OeX5RfSNklD\n",
       "iEWk/vMtsLDwhV8IKz774iMsjAfaRZPn5yKrrnt48HCrKPY3txUrfKzAiBFEFxYZG5dIPROeWcDf\n",
       "XvoVn7PbB6MbcmeAl2sUNAECA5ncqnQEbRMrLHr+V/zrsBGvpo2IURz6G/21115j6NChFR6Lj4+3\n",
       "fx4XF0ecszW5chVHj9rm455Tdv6auJ3TAd6s8PVgSkEJAJPSTxocketKTEwkMTHR6DBE5CJMVltD\n",
       "vLapZ8u03t7w3nscnjWZCGNDuyR5nh7Mnd6JpQu2E3raDCdO8I8zOczMi+KMv4sUXEScWEOLhUXP\n",
       "/0KjHFsPr6xAb+bM6EzuUz8YHNmlSWvgzWPTOvHc0zvwKbbS6sgZ5v1zN/d4hRkdmkitcthvwk2b\n",
       "NrF8+XK+/vrrCo+XLVRIDbz4Yum6z3372hpziVt70c+TPxWW4GmFfjl58MMPcPnlRoflcn5fQF2w\n",
       "YIFxwYgIcUPi7O/eJacmE3G2DPG3PEu5hni88gr073/J16lIclIysb1iq3RuVWMPDw0ncUNihecd\n",
       "a+zLow924rkndtDAaqVdQRGPLt3FnBkV9wUTkSqyWHj2YBqts20FzULgsQc7kRHma2xc1bSzXTDP\n",
       "TryMOf/6DYC+P53gz+FaMUjqN4es+vHzzz9z7733snbt2kqniUgN5eTA0qWl2xpNIUCSp4kvejct\n",
       "3fHss8YFIyLiIGWHG5/ryD/4q3Qeyi+xn/NaeKitO/4lXudCLFiqfG5Vn/NiQ6V3tQ1mXsvSgkif\n",
       "X07yp7cPVPu5RQR4+GHiss/YN+8P8OTXdsEGBlRz/70ygmf8Sl+6Tco4Ca+9dsnXOVeQVc8JcXY1\n",
       "LlSkpKQwYsQIVq5cSdu2bR0Rk9u7YNOaV1+F7GwAUv396PjEX5VkBIC3ry+zVOmaNZDsROuBi4g4\n",
       "QKe92cx+fY99+5tujXkuuomBETnOx42DYe5c+/bozw4z6rhWAhGpltdeK9fP7c0bmvOmr6eBATnO\n",
       "Y/6ebL68zJSP+++HL764pGuULciq54Q4s4sWKsaNG0e/fv3Ys2cPMTExLF++nGXLlrFs2TIAHn/8\n",
       "cbKysrj//vvp3r07vXv3rvWg67sK34kxm2HJEvs5rzYJoum0SCUZAWBvy0B+iG1k27BYyv2siIi4\n",
       "uhYWK3976Ve8LbahzgejG7LwvlgOJafYC/vJqS5eoH38cT4rsxLIYynpcJG+OerGL1Jez5w824v3\n",
       "s766PIzXRrYyMCLHsppMLJoca2/Ei9kMI0cSU6BGvFL/XLRHxVtvvVXp8VdffZVXX33VYQG5qwvN\n",
       "oT03POvGE9n8PfWo7eQmTfiwcTCaZCNlvX19DJfvPvsO3Kuvwvz5oKlYIuLi/POLee90MY3OFimO\n",
       "mWDOjM7k+3nZ3xkEODjbxVc98vDgkVZRtDyZxh+Sc/G2AiNHwtatF3zIuTc2ANIT0usoUBHHq2pf\n",
       "l8pEHstnyd4UONu64ScvE09MjsXqoBU+HBGjIxT4ejJ3eicSHv6OJsUWeyPeGWrEK/WMQ3pUSM1d\n",
       "aA6tBQsRU8K5z5JTevK0aRR66Fsn5W3rHMpevwa2jTNnyvczERFxQR4lVub9czedzhYpirxMjAny\n",
       "ctmGeBeT7+nB3OmdORF8djHFkyfhppsILK5+vwwRV1DTJTAb5hXzxPO/EHa2SHEyyJuRgV4UOHDK\n",
       "hzMt03mssS/T2kZDA9vffW0Linhs6S48LGqwKfWHXu0aqOyQzcqGrPbYmUXblFzbhr8/PPBAla6v\n",
       "ZjluxmSyNZY76+SCeLr2uEzffxFxWZPXHKTvT6UrfCyeeBnfetfvP10yQxswb3onCkxn3wX+7Tee\n",
       "O5imFyAiF+BptfLo0l20SssDoMjbg0cf7ESqp2NGUjirnwL8YPly+3bvX05yvxrxSj1Sv3/bO7mq\n",
       "diK/dV1q6cbdd0PjxlW6vprluJ91oUHQrBkAoUVmxnc16fsvIi5p5PFTjF1f+vvvzRua89mV1Vsu\n",
       "1NX81jqIOa0i7dtXnT7DA2/tNzAiEef1UOox+vxy0r79zKTL2NXWtVf4qLLbboN58+yboz47zGg1\n",
       "4pV6QoUKJ9e1uISeO7MAsADMnGloPFL7yo6EudTmcGYPE8yYYd8euz4VU4nehRMRF/Pll7Zmkmd9\n",
       "6GOqVw3xqmJdaJCt19BZI/93hGGfHzEwIhEn9MorTDiWZd980s+DjX3DDQzIAAsWsCEk0L75aEo6\n",
       "bNpkYEAijqFChZObWWa9+A0hgdDKvf5Qc0dlR8JUNtLmgiZPhqAgAJofzSs3bFpEpC6ULbg2imx0\n",
       "adMQDx6EESPwOVtj3d88gImBXg5riOcqkpOS6fDxaj4t8wLkwZX76Xv6jIFRiTiRTZtgyhT75pc9\n",
       "wljgXz+WIb0kHh78tWUke1rYVgKxN+Ldt8/YuERqSIUKJxaeWcDowtJCxWsRVZvyIW4uKAjuu8++\n",
       "OXZdqvqViEidKltwzS/Or/o0xOxsuOkmOGErsJ4M9mHu9E6cMblXkQJsX8PwaZG8+FQ3vvey3b9n\n",
       "iZUlB47A3r0GRydSNy7Uz61FQZHtxXhxMQB7WwTw5ORYrPUkV1S1j905+Z4ezJvemcxGZxvxZmWR\n",
       "0q0rnNI0EHFdKlQ4sZGfHbavH/tDbCN2NayfXc6lFkyfTtHZ39Vd9mbTw2xWvxIRcW7FxXDrrbBr\n",
       "FwCFJhOPTuvIscbu/buvsIEnowO9OH72BUiwpQRuvBGysi7ySBHXV1E/t4Z5xfxj/2H7/4Hj3p7M\n",
       "nd6Zggb1ZzRFVfvYlZUZ2oBHH+xE/tnt5nn5MGaMvZgj4mpUqHBSAWfM3PjFUfv229fHGBiNuJxm\n",
       "zfgktLSR1Kx8LW0nIk7uoYdg/Xr75ryWEe7TEO8i0jxNzJvemQKfs3+27dsHo0fjpR5E4mY8LFbm\n",
       "v7yT1gVFth2+vkxpG01maANjA3MSv7UO4p7AMgWb//5X/e3EZalQUQfKDt+q6rD7YZvS8Cu0vbg8\n",
       "GN2QbZ1Da9RksSaPFde0PKJ0qdKbi6w0S88zMBoRkUq88go8/3zp9ty5fNxYRYqy9rYK5Kl72pfu\n",
       "2LiRv6ZqhJy4lylv7afXzjKjiV5/nV8a+hkXkBN6t4EnK4a3LN2RkMC4YxqBJa5HhYo6UHb4VlWG\n",
       "3ftYrYz4b2ln77eviwGTqUZNFmvcoFFczn6/BmzpYitWeABjNhw2NiARkYr8riEeI0bA448bF48T\n",
       "+6J3U16ICrNv33b8FDdv1Eog4h4m51sY8b8yP++PPWabLlaLXPWNvjeGtSjXiHdOSgaX71SxQlyL\n",
       "ChVO6LbCEhpn24a0HfaAz69oWun5rppEpfaVnTJ03VfpNDpdZGA0IiK/s29fuYZ4dO8Ob7wBHvrz\n",
       "5EL+Gdm43IuzaW/up+evJw2MSKT2Xb4ziyVnSt9oWxcSWG753triqm/0WT1MzG0ZCT17AuAFxL+8\n",
       "k5ijGl0rrkN/CTgZU4mVmWX6CST4elLsVfm3yVWTqNS+He0bsaelraLuYy5h+P/0zpuIGOdcYT1u\n",
       "SJytG/1NN5U2hYyIgLVroWFDQ2N0eiYTLF8OvXsDtpVA5v9jF63yCw0OTKR2RKfnEf/yTnuD+T0t\n",
       "A5nTMlIFzYso8PSADz+EqCgAAvOKeeL5XwhRbxtxEfof7mSu+OkE7c/WGs74evKar75FUgMmE6vL\n",
       "jKoYvvEIfpaSSh4gIlJ7zhXWM0+kw9ixsGeP7YCvr+0P6uhoYwN0FX5+8MEHHPW2vXQLyCtm6f7D\n",
       "9mVdReqLoGILi5b8QmCebdTV8UY+zJveyfYi3EAuM5o5KgrWriXfw7YUXExGPm/mFONZXL2/BbXc\n",
       "vdQlvQp2MmPXpdo//2hgFKc96sd60GKcL3s24dDZ/+nBZ4q55US2sQGJiNt7OPUYfPZZ6Y4VK+wj\n",
       "BKSKIiOZ0i6a/LMrgbQoNMOoUVCkKX5ST5jNLDlwhJgM24KbecC86Z3JDDF+hQ+XGs3cowePtIy0\n",
       "b15jtjLtzf1gvfSRFWXvW8vdS21TocKJxB44Tde9theRxZ4m/jNI7yxJzZV4mnjRr3SpqrvST9rn\n",
       "g1dnRRoRkZoY9vkR7ijbgf6xx2yjKxzImd7trM13IHf7+7LovtjSHYmJMHu2Q59DxDB/+Qv9ckp7\n",
       "Ktwd6MXeVoGVPEAu5LPQIJbf0tK+ffOmNIZvTDMuIJEqUKHCiZQdTbHxiqZaE1ocZoWvB9kNbUOE\n",
       "Y4rM8N57wKWvSCMiUhN/LCrhwZX7S3eMHl0rDfGc6d3O2n4H8qseTfjXqFalO/7xD0LMxQ5/HpE6\n",
       "deIEJCTYN5ff0pL3GrjuyxZnKJ7+e1gLNvYpbdA/9c199Ms+Y0gsIlXhuv/j65k2Fiv9tx+3b799\n",
       "XUwlZ4tcmjyTiQ+vaVa64+9/r9aQPxGR6opOz2NVTjGe5xq59ehhm/Khhng1tuqG5uxo6GvbsFgY\n",
       "dCrH2IBEauqDD+yjP/e0DOTfw1oYHFDNOEXx1GTimbsvY5uXbVq5pxWWHDwCu3cbE4/IReivAyfx\n",
       "YL4Fj7N/u633NnEoJsDYgKTe+eCaZhR5n/0v//338MUXxgYkDjNp0iTCw8Pp3LlzhccTExMJDg6m\n",
       "e6MrqI8AACAASURBVPfudO/enYULF9ZxhOLuAs6YWbTkF0LO/p7L8PayNc/09zc2sPrCZOKT0CD7\n",
       "5vUnVahwNsrTl+jtt+2fbryiqW21G6mxIh9PRgd5cezsqO0gS4lt9SU14hUnpEKFEwg+XcSEgtLu\n",
       "u0vK9BMQcZSsYB82XBleuuPvfzcuGHGoiRMnsn79+krPGTBgAD/++CM//vgj8+bNq6PIRMDLaiX+\n",
       "5V32hngFPh6M8Pckdvi15/VtKNs3x+jeErWhNod/bwgJtL+Y65WTR0i2mmo6E+XpqgsxF8Pnn9u3\n",
       "E3s1MTAa13WhfJPuYWLu9E72RrwcOAAjR6oRrzgdFSqcwC0bj+B39vM9LQJI9FbVWGrHmutisJfE\n",
       "Pv2UtvmFRoYjDtK/f39CQkIqPceqqT5iBKuV585Y6LGrtHnmU/e053tva4V9G8r2zTG6t0RtqM3h\n",
       "38d9vKF/fwA8gau/P175A6ROKU9X3bWncuHs/48fGvpxvLGvwRG5psryzf4WgeUb8X7xBUydqmnB\n",
       "4lS8jA7A3TUotJTruvv20Obwzv5KHiFSfYcj/NnYKIBBp3IBmJh+kpdw7XmfcnEmk4lvvvmGrl27\n",
       "0qxZM5599lk6dOhw3nnx8fH2z+Pi4oiLi6u7IKVeuvbbY9xXZsRgvL8nX/RuCmv0e65WjBkDX34J\n",
       "QNy2Y+V7E9UDiYmJJCYmGh1GrVCeLnX9ydP2z9eHapWP2vJVjyY816wJs46cLWr+61/Qrx/cdZeh\n",
       "cYlrc2SeVqHCYNd9lU5wrhmAo2G+fNGziQoVUm3nhvkBJKcmE0HEeecsjwi1FypuPJnNW1mFTrEm\n",
       "udSeyy+/nNTUVPz9/Vm3bh3Dhw9n7969551X9g9gkZpqUGhh8jsH7dsb+zTlyf1Z9DMwpuqqSm51\n",
       "CiNHwoMPQkkJXfZm0zirkHSjY3Kg378wX7BggXHBOJjytE1IdhG9zy1JajKxISRQw79r0b8iQpk1\n",
       "cAisXGnbMWeObTWmhg2NDUxcliPztP7vG8jDamX0+tIlSd8dEk2Jp6Z9SPVVZVjxjgB/W8Uc8LHC\n",
       "iP8erssQxQCBgYH4n21aeP3112M2mzl58qTBUUl9N+qzwzTJsk0vOxHsw7MTL3PZhnhO0bG/KiIi\n",
       "YMAAADysMEDTP1yG8rTN1d8fx96p7aqrOObjXeF5zrDcp6MZcU/JySl037nN1uAY4OhReO65Onlu\n",
       "kYtRocJAg7JyaHa8AIATJvj06kiDIxK38Ze/2D+9aVMa/vnFBgYjtS0jI8M+93nbtm1YrVZCQ0MN\n",
       "jkrqs7ASK+M+SbFvr7ilJQW+ahRdJ8b+P3t3Hh5VefYP/Dtb9pCdhCxsEkgQZJHFDRhUCLigCALW\n",
       "Wq1vLbXy+uqvWn21Vaj70lVai/V1q4ogomDFgAsBRdnDviQEEpIAgZA9k2TW3x9n5pwzkD2TeWb5\n",
       "fq6r13WeyRm8LfHMmfs8933Plw+N25mo8Be8TkuMO1S/s6rf5Qv5TfKwC0T8O9lgQ+z/pOLduy5R\n",
       "Xnz5ZaCiou03EXkJSz9EcThw7xklU74sTIvmUN7EkZfcfDMwbBhw9Ciimmy4cdNpvIbWn1qQ77vj\n",
       "jjuwadMmVFZWIiMjA0uWLIHFIpWULVy4EKtWrcLrr78OvV6PiIgIfPTRR4IjpkBhzDHKzTDVJRFP\n",
       "mGyIdPamOKID1k1iIr49riepHikrue02WH/1K+gBjCysRcpliR6JkXqG1+mOJVS34LKjNdJCq5VK\n",
       "md5ZKjaoILH+mhTM/vAEMpvNQEMD8Ic/AH//u+iwKMgxUSHK5s24zCTtpjAbtHg9XIchgkOiIKLV\n",
       "Ar/5DfDLXwKQtmi/PnCg2Jio25YvX97uzx944AE88MADXoqGgolrSgcAHH9E6keRWtGEX6oaaD4R\n",
       "oWdZYwdcT1Jd/x/2SFIStvWJwNV1Up3/9Or6nv+Z1GO8Tl/swkTn/Tut0LqGTkyZIpUykVfYtRq8\n",
       "mt4Xy445y4GXLZP63QwbJjYwCmos/RDllVfkw/VXJ+Osljdx5GV33YVzemkXT9+qFtxQXdfBG4iI\n",
       "OvaLVcfl/Vl7h8bgixB+vnnbl3F95GP1BAUiX3LhOOKp6lKlefPEBRakNsdEAlOnSgubTWqsSSQQ\n",
       "ExUiHDoEfPEFAMCuAVbOyBAcEAWlsDB8kKzMdL/3TBXnZxNRj2QX1WGqqsZ82fxL/LaBZlf5UnO/\n",
       "r+OiYXXuYhnd2AwUFwuNh6gjaTYHRhbWAgBsgFT2Qd6l0Uj9KVxWrwZ++EFcPBT0mKgQ4dVX5cMt\n",
       "YxJRlhIhMBgKZh8lxaHJ2RtlWFMLsGGD4IiIyG85HFi4okhebhyfhMOX9GnnDYHFl5r71ep12DVc\n",
       "SUTj44/FBUPUCbeZlXKxbX0igKQkgdEEsXHjgDvuUNaPPsqHWCQMExVelmS2KLOKAayYyd0UJE6t\n",
       "Xod1k1U1oKqSJCKirrjJ7MCoAumJqBnAm3MHiw0oyG2c2FdZrFwpLhCiTpjboiQq1sUFT4LTJz33\n",
       "HBASIh3/8AOur2kQGw8FLSYqeokxx9jqFtBZhSWAs8vzjwYtDmbGiAqRCADwcU4GbK4eKd98A+ze\n",
       "LTYgIvI7WpsDz5uUMcdvhGlxKjlcYES0ZUwCLK4mpjt3AkVF7b+BSJDkymZcYZWe2lt1GnwdFy04\n",
       "oiA3aBCwaJG8/E3ZWeis9nbeQNQ7mKjoJRc2CAKA8CYrftGs3Mj9MYz/95N4FYlhyBuv2mLJXRVE\n",
       "1I7WEvE3bD6NYc5qh4ZwHV6I4Lht0RoiDdgxMl55geUfJIj6mmHMMV708ymqvja7hsehVs/rh3BP\n",
       "PgnExgIABrZYcNOm04IDomDEb8pedNOm04h1lnmdTAnHf9gJnXyEWwnSxx+z8RoRtenCRHxYsw0/\n",
       "/6xY/vnyG/ujkpOsfIJbEnrFCnGBUFBTXzNc40jVpm4/Kx/nTWBvCp8QH+829ePuz4oR3mRt5w1E\n",
       "nsdEhZforHbM2VAmrz+ekQFHkHRCJ99XODAaP0Y7m7rabMCf/yw2ICLyG/NySxFfawYAnIsLxSfT\n",
       "0gVHRC5bxiaixXWvsWcPUFAgNiCiC/Q724SsE/UAAItOg+/HJgqOiGT//d9A//4AgLh6C+Z/WSo4\n",
       "IAo2TFR0Q0db2Fozdfs5JFe1AACq+hiw/uqUDt5B1DvaGqH3okbJlDf9fSlQVSUiPCLyI8l2Bxao\n",
       "bl7fum0gWkK7tm3bl8Z6BhpTuB7fxUQqL3SiqabrHqez9zdEPWFUlX3sHBGPhkgDrwm+IiwMePZZ\n",
       "eTkvtxT9bJwAQt7TbqLi3nvvRXJyMkaOHNnmOQ8++CAyMzMxatQo5OfnezxAX9TRFraLOBxYsO6k\n",
       "vPz0+nRYDMwRkRhtjdDLNThQlC7d0Ibb7MDrr4sKkYj8xO9MNoS3SNeRAzoNNnQjCe9LYz0DUa66\n",
       "MWEnEhWue5xO3d8Q9ZCxlbIPXhN8yJ134nB4KAAg3GzH7038+yDvaffb8s9//nPk5ua2+fN169bh\n",
       "2LFjKCwsxBtvvIH777/f4wEGgmkWBy4pawQANAJYe22q2ICIWqPRYKW6V8VrrwHNzeLiISKf1v9U\n",
       "I+5tVjrBPxGpg529KXzOxtgo6ckoAOzfDxw+LDYgIqcBzWYMLZFGX7YA2DKGZR8+R6vFK+nKqON7\n",
       "WuwYWN4oMCAKJu0mKiZNmoS4uLg2f7527VrcfffdAICJEyeipqYGFRXMwF/o4SYl+/hOmBZ1UQaB\n",
       "0RC17duJfXEuTsqco6ICv88axO2/RNTqpI/7Vp2A3vnzXcPjsN7AJIUvMul0wA03KC90YlcFkTfM\n",
       "qK6TjzeEaNAYoW/nbBLlx5hIbHdOENIBuO/j42IDoqDRoytCeXk5MjKUJ7Dp6ekoKytDcnLyRecu\n",
       "XrxYPjYajTAajT35R/uNzOJ6XGeR6rlsGuBv4TpwPwX5Kqtei1XT03H/iiIAwH3mOnxy/ozgqLwj\n",
       "Ly8PeXl5osMg8kmucgAAOP7IcYw8WoNrdlfKP182bzCwdL+o8Kgj8+cDq1dLxytXAk8/LTYeIgAz\n",
       "qurl449DWBLdVa5eHgBQUlqCFPSs/536z0uOT0be+jz5Z2/cPhjjDlRB6wCu2nMeo47UIDjuDkmk\n",
       "HqcuHQ73piqaNiZZqBMVwWRertJkbNOEviguqmGignzaf4z98JOVRYhxAP1Pm3Bpwwn5g+t02Wn0\n",
       "S+8H4OIPMX93YQJ1yZIl4oIh8mUOB361Unmi9tWVySgcGN3OG0i4G28EIiIAkwk4dAg4cAAYMUJ0\n",
       "VBTMjhxBVpPUZL7FoMUXIVpcJjgkf+Pq5QFICWRP/nlnlrqnIYr6R2HD1SmY8b30+q9WFGFDPL/R\n",
       "UO/qUfoyLS0NpaXKF/GysjKkpaX1OKhAkVzZjKnblW7GK9T1/0Q+yhSux5thyqXhoSaL3NSqydrU\n",
       "tUayRBRwZpsdGF4kbdluAfB/cwaJDYg6FhkJ3HSTsmb5B4mm+h3cdlk8Gtjfxue9NXsgXJ3Lsk7U\n",
       "Y0Z1fbvnE/VUjxIVs2bNwnvvvQcA2Lp1K2JjY1st+whWczeUQWeXdpzszo5FAZ84UQ94c1zX0jAd\n",
       "LDrppuFqqwPDj9X26j+PiPyD3mrHs43KKON/hGtRkRgmMCLqtHnzlOMVKwDVjtjWepAQ9QbXvUzh\n",
       "C8/Jr22c0Ledd5CvOJcQhtfCla+OD5edA1paBEZEga7dRMUdd9yBq666CkePHkVGRgbeeustLFu2\n",
       "DMuWLQMA3HDDDRg8eDCGDBmChQsX4h//+IdXgvYHfaw23LjptLzmbgrqKW+O6zql0+CbK5Wk4/wv\n",
       "S9s5m4iCxc0bT2GIc9BHfYQeL4XrxAZEnXfDDdLOCgAoKAD27ZN/pB67znGQ1JtssOGK2dHIbDYD\n",
       "AJpDtNg6OkFwVNRZr4TrUBspdQ7IMFs4yp56Vbs9KpYvX97hH7B06VKPBRNIFpyrdpst7+qWS+Qv\n",
       "VszIkGsRr9ldifQzJsEREZFIkSYrfrZWedr+/s0DUP0Nk5h+IzwcmDULcN3brVgBjBolNiYKSsZt\n",
       "Z+XjH0cloDmUCU9/UavV4N+3DMCiD49JLzzzDHDPPUBsrNC4KDCxxW5vaG7GTyuq5eWfw7VAG01G\n",
       "iXxVcXoktl4mJdi0DuD29WWCIyIikRasO4nYegsA4ExiGD69nj2pfEmnygPnz1eOV650K/8g8gqH\n",
       "A1N3KP3bNk5k2Ycvau96subaVJQnOUv+qqqAF18UECEFAyYqesP77yPJKu2mOBcXihWh/L+Z/JO6\n",
       "ZGnG92eQZOdNLVEwSjZb3JKVb84ZBIuBn22+pFPlgTk5QJ8+0nFREbB7t/cCJAIw0uZA/9PSDs0G\n",
       "gDuOfVR71xOrXos35w5WXvjLX4CTJ70cIQUD3mV4mt0OvPqqvFw1PR0W7qYgP7UnKxY79dLvb4jF\n",
       "jvubWLtMFIwWnapEqEVqTpGv0+BbPgX1T2FhwC23KGtO/yAvm9til4//E6pFC8s+/NKm8UnYF+Hc\n",
       "VdHSAjz1lNiAKCAxUeFp338PHD0KAGgI1+E/xn6CAyLqAY0Gf1J1eL632Q4Nd1UQ+TzXFAdjjrHn\n",
       "f9j+/ZhdqUz++d9IHRwcJei/1NM/WP5B3uRwuCUqVoXwa4i/cmg1eDVDlbB+7z1g714A7lOEPPIZ\n",
       "REGLVwhPW7VKPvzmimSYwtvtV0rk8z4L0aI62gAA6OcALj1WJzgiIuqIa4pDRVVFz/+wxx+H65nn\n",
       "tpHx2MgvF/5t+nQgJkY6Li4GduwQGg4Fj8ySBnlqUGOYDhtCmPD0ZzuiI4CbbpIWDgfw2GMA3KcI\n",
       "eeQziIIW7zY8yW4HPvlEXm4anyQwGCLPsGk0+P7yRHk9Zee5ds4mooDy7bfAunUAALsGeGPe4A7e\n",
       "QD4vJASYPVtZr1ghLhYKKlO3K9M+toxNRAtLo/3fiy8CWufXyfXrga++EhsPBRQmKrrAtZWpzW7a\n",
       "27YBp04BAKr1OuwdxlE9FBg2j1OSbpN3nmP5B1EwsNuBRx+Vl+uvTsHxjCiBAZHHqMs/Pv4YGpZ/\n",
       "UG9zOGDcrjzoyOPDvMBw6aXAvfcq60cf5fWEPIaJii5wbWVqs5u2quzj69go2HXMFFNgyM+KRV2k\n",
       "VMbUt6oFWSfqBUdERL1BXVv8zOhL5akQzRoN3rptkODoyGOuvx6Ii5OOS0txWWOz2Hgo4A07UY9+\n",
       "ldLvWUOEHjtHcNpHwFiyBIiIkI737sXNVSwRJs9gosJTHA6c+cff5eX71iaBwRB5lk2vxZYxSvnH\n",
       "JJZ/EAUkV0I+Y2Ff3Hu0SH793eR4VMaHCoyMPMpgAG67TV7O5BcL6mVTVbspvh+byPHGgSQ1FfjN\n",
       "b+Tl/5Sfg8Fib+cNRJ3Dq4Sn7NqFlOYWAEB9hB7f6LjtiQKLuufKlJ3n2CmeKIDd+k050swWaZGQ\n",
       "gDdT+PQz4MyfLx/OqK5nSR/1HocDRlV/io0TWPYRcB59FEiS/l5TzVbc9lWZ4IAoEDBR4Smqso8t\n",
       "YxNhYYMgCjC7h8eh1vlrnXquGdmmFrEBEVGviGq04Kefq3oxPfUUGvS6tt9AXlVSXCKX57TZM6sT\n",
       "rnv5WVQ5/16TLVaMKKxt81yOG6SeGNXYjOQq6Z6hSiPdT5D/U1+LjHNvBhYvln/20/+cRJ8Gi7jg\n",
       "KCAwUeEJDofbtI/NqgkJRIHCYtDiC9VYwunV7FNBFIh+8p+T6NNolRaDBwO/+pXYgMiNDTZ59F+b\n",
       "PbM64VTNWXw/KVleG3e0XdLHcYPUE+rSos9CtLDq+fUjEKivRRVVFcB99wGZmQCAKJMVd37e/UQq\n",
       "EcBEhWfs2wccOwZAmgvNBkEUqFarEhU51fUs/yAKMKktFsz5ulx54YUXpHGWFJDUkxem7DgHLcs/\n",
       "yNPsdul+wemTUH71CFgGgzSu1OnWb8qR1mIWGBD5O14tPEFV9vHj6AQ2CKKA9VWIBk2h0lbhQS1m\n",
       "4OBBwRERkSc9WH4OIc4maHsjw4DbbxccEfWmvVmxqOpjAAAk1JoxsqDt8g+ibvnhB6RYpB1atVEG\n",
       "bDSwNDqgzZ6N3ZHhAIAQqwMPlVcKDoj8Gb9Re4K67GMcGwRR4GrWaLB1lGrHkCpJR0R+Lj8ft6i2\n",
       "aL+a3hdgv6WAZtdq3O5bpm47287ZRN2wYoV8uHlcImy8pgQ2jQavZCjXlJuq6oCdOwUGRP6MiYoe\n",
       "uqSpBTh8GABg0mqwfSTLPiiwbVIn45ioIAoMDofUtd1py5gE7IyOEBgQecvGiX3l48k7z0HHkj7y\n",
       "FJvN7T5h44S+7ZxMgWJPVIR7v75HH2WpMHULExU9NE1Vd7c5JgotoeyMToFt22UJaHGVNx08CBw5\n",
       "IjYgIuq5DRuAb74BANg0wBu3DxYcEHnLgcwYnHJe0uPqLZhi6fwXCk4DobYYc4z42aWDgTNnAABV\n",
       "fQzYOyxWcFTkLf+6fTBsWufumbw84MsvhcZD/omJih5SNwjaEBctMBIi72gO02HbZaqdQ6rSJyLy\n",
       "QzYb8Nvfyst1U/rhZGqkwIDIm+xajVuj5Dkt9k6/l9NAqC0VVRW4Lc0qrzePS4Jdx7KPYFGWEoHP\n",
       "jf2UF377W+mzhqgLmKjogbQzJmQ1SXOhERaGTTG8saPg4NaLhYkKIv/2/vvS9CpIJYzv3DpQbDzk\n",
       "datUkxhmm+3QWTufrCBqjc7hwBTVyNs8ln0EnfduGYhGrWoH7rvvig2I/A4TFT0weZeqk21ODkw6\n",
       "ln1QcPhxdALMroZY+flAUZHYgIioe5qagN/9Tl6+nRyPqthQgQGRCFv1GpyNl/7eExzAmMM1giMi\n",
       "fze+3oS4egsA4JQW2D80RnBE5G3VMSF4M0W1A/f3vwcaG8UFRH6HiYoeUGeKMXeuuECIvMwUrseW\n",
       "PqodRNxVQeSf/vpXoKxMOk5Oxluqm8qS4hK5/0BJaYmgAMkbHBoN8sarpn9s5/QP6pmZqglCn4Zo\n",
       "Ydey7CMYvZscD/RzloCcOoW/DBvInjbUaUxUdFNyZTOGFTv7UxgMwE03iQ2IyMvcerIwUUHkfyor\n",
       "gRdeUNaLF7vtDLTBJvcfsLG2OOCpt+ZP2lUJg51d+qmbLBZMq2mQlx+H8utGsGrSaYE//EFe33e+\n",
       "Glk/i2dPG+oUXjm6afJO1W6KadOAWHYypuCyMTYK0OulxfbtwMmTYgMioq559lmgzvnUc9gw4L/+\n",
       "S2w8JNThwdE4kyCVf0SbrLiyjlu0qZs2bkScVUpunosLxVY9d1MEtXvuAYYPBwBENttw11ru0KPO\n",
       "YaKim1j2QcGuVq8DrrtOeWH1anHBEFGH1KMkRydFw/y3vyo/fPFFaXcgBS+Nxm1XxczqunZOpmDR\n",
       "lRG0rnNX3TlPfi1vfBIcGiYqgppeD7z0kryctfEUBjSbBQZE/oKJim5IszlwaZH0AW4FgFmzhMZD\n",
       "JMycOcrxqlXi4iCiDqlHST5RZ0KIc2f/rqhw4JZbxAZHPmGjKlFxXU0D0NIiMBryBV0ZQVtRVYH0\n",
       "X/XF9CZlN87GiZz2QQBuvBHboyMAAHqbAw+Vn+vgDURMVHTLLWZlbNe2PhFAQoLAaIgEuvVWwDV6\n",
       "assW4NQpsfEQUYeyjtdhnupz7JX0vgCfeBKAgoFRKHJe0qNtdmD9erEBkd+5/GA1+jRaAQBnEkJx\n",
       "eHB0B++goKDR4NV0pWHvjOp64McfBQZE/oCJig6ot7y5up7f1qLc4Lk1FCQKNklJwJQpyvrTT8XF\n",
       "QkQdcziwcIUyTnjTuCTsjQoXGBD1NvX0lth+se1PctFo8Im68eHKld4LlAKCUVUanTeBSVBS7I8M\n",
       "x7fqHTaPPgo42LSX2sZERQfUW95sNhvias242ir9R2XTAN/EMlFBQU7do4XlH0Q+7co95zH6aC0A\n",
       "wKrT4F9zBwmOiHqbenpLk7Wpw0kuq9SJijVrgKYmL0VK/s5gt+Oa3ZXyWj3ylggA3pwzCBadM3m1\n",
       "ZYt0jSFqAxMVXTRp1zn5/7R9w2Kxu7ycc+YpuM2erTwx2bwZOHtWbDxE1Cqdw4FffnxcXq+dmory\n",
       "lAiBEZEv2qvToDTZucumoQHIzRUbEPmNq+saEWWSyj6Oa4Gjg/gwj9yd7huOz65LU1547DHAYhEX\n",
       "EPk0Jiq6aPJOJVO8eVwS58wT9esHXH21dGy3A599JjYeImrV7MpaDDxlAgDUaYB/zxogOCLySRdM\n",
       "/8CKFeJiIZ+nLpGeXHZGfv2TUC3LPqhV788agDqd8ytoQQHwf/8nNiDyWUxUdEGi3YHRR2rk9XeX\n",
       "JwqMhsiHsPyDSLjWeirJGhvx4CmldvzVcB1q+oR4OULyFxsnqLbsf/45wmz2tk+moOYqke7/yyTc\n",
       "1KI8sPs4lF8xqHV1UQa8kaIaRPD000B9vbiAyGfxKtIFN5vt0Nml/hT7M2NwPi5UcEREPuK225Tj\n",
       "b78Fzp8XFwtRkLqwp5KbP/8ZSRbptXOxIfhbOD/+qW0n0iNRFOZMZJlMmFLbIDYg8nkT9lch2tkX\n",
       "sSw5HHt13E1BbXs/OQ5IT5cWZ88Cf/yj2IDIJ/FOpQtuVU372DyOuymIZBkZwMSJ0rHNBqxdKzYe\n",
       "IlLU1wN/+pO8fPu2QWjilmxqj0aDL+P7yMsZ1XzaSe0zbld2bG3ktA/qQItWCzz7rPLCX/4C1NaK\n",
       "C4h8EhMVnRTVaMF1FmWEzuZx7GRM5EZd/vHJJxf9WL0t3Zhj9F5cRMHu9deB6moAQHnfcKy/OkVw\n",
       "QOQPclXj16fUNiCsmX24gp161K36czy0xYar9ig7KfMm8B452Kh/Nzo9XOCnPwWGDZOOa2vxp0sz\n",
       "eX9Ibpio6KSr9pyHwXm8Q6/B2YQwofEQ+Zw5c5TjDRsuyoyrt6VXVFV4OTii4BRqt7ttqf3wxv6w\n",
       "c0s2dUJReCgwYgQAINzuwJV7WdIX7NQN5NWf4xP3VSHc2Z+ipF8EjqdHigqRBOnWcAGdDnj8cXl5\n",
       "b10N6s6d7qUIyR91mKjIzc1FVlYWMjMz8dJLL13088rKSsyYMQOjR4/GiBEj8M477/RGnMJN3qFs\n",
       "aVsdwvwO0UUGDQLGjpWOLRbg88/FxkNEmHuuRh4ZfNqgx4arkwVHRH5l3jz5cOo2jp6m1k3drvxu\n",
       "5E1IYtkHdd6dd6I8RHoUHFtvwe2VNR28gYJJu9+4bTYbFi1ahNzcXBw6dAjLly/H4cOH3c5ZunQp\n",
       "xowZgz179iAvLw+/+c1vYLVaezVob4tosmL8gSp5/Rk7GRO1roPyDyLyHr3VjnvKVZM+wjSw6vn5\n",
       "RV2gSlRM3F+FiKbAur+j7nNt9a8sKcYVe9VlH33beReRRC4VueoyvKyaTXDvmSqgpUVcYORT2r1j\n",
       "2b59O4YMGYKBAwfCYDBgwYIFWLNmjds5/fr1Q11dHQCgrq4OCQkJ0Ov1vRexAFfsPY8Qq9SforB/\n",
       "FI5z2yxR69TlH7m5QAM7xROJMu2HCqQ7J1VVRxvwf5xGSl01bBgwahQAIMRix5V7WP5BEtdW/+nN\n",
       "FoSZpWbzB3UaFKex7IM6pi4VeTsEOB8jfUAlW6zAu+8Kjo58RbsZhfLycmRkZMjr9PR0bNu2ze2c\n",
       "++67D9deey1SU1NRX1+PlStXtvpnLV68WD42Go0wGo3dj9rLpqjKPjaNTwI2lQuMhsiHDR0KjBwJ\n",
       "7N8PNDcD69a5PZHzZXl5ecjLyxMdBpFH6BwO/OSLk/L64xkZaNpYJjAi8lvz5gF79wKQyj8+0LNR\n",
       "IiluV03EW8Udx9QNLRoNVs7IwP0riqQXXnoJuPdeIMAefFPXtfsboOlEjdnzzz+P0aNHIy8vD0VF\n",
       "RZg2bRr27t2L6Ohot/PUiQp/Em6zY8JBpexj8zgmKojaNWeOlKgAgFWr/CZRcWECdcmSJeKCIYI0\n",
       "KcfVsC45Phl56/M6/d45ZjvSzzcBAOoj9FhzbSrARAV1x7x5wJNPAgDGH6hC9Ih4wQGRrwhvsmKG\n",
       "WZmItypEi0SB8ZD/Wjs1FT/5TwliGq3A8ePARx9JU0EoqLWb+kxLS0Npaam8Li0tRXp6uts5n889\n",
       "YQAAIABJREFUP/zwA26//XYAwCWXXIJBgwbh6NGjvRCqGJNqG9y2tJX2ixAcEZGPU/ep+OILwGQS\n",
       "FwuRH+vupByN3YHHTMpTztXT0mAK55Mp6qYhQ3AwQioiD7E6cG0NS/pIctWe83DNwDuWEYkCPUuj\n",
       "qXuaw3T4ZLrqO+bzzwN2e9tvoKDQbqJi3LhxKCwsRHFxMcxmM1asWIFZs2a5nZOVlYWvv/4aAFBR\n",
       "UYGjR49i8ODBvRexl+VU18vHq7mljahjw4cDWVnSsckErF8vNh6iIHPVnvMYYZOecjYAWD0tvf03\n",
       "EHXgy/g+8vHM6jqBkZAvcZ/2wSaa1DOfXp+GBq3zu9bhw8Cnn4oNiIRr95u3Xq/H0qVLkZOTg+HD\n",
       "h2P+/PnIzs7GsmXLsGzZMgDAE088gZ07d2LUqFG4/vrr8fLLLyM+PkC2BTY1YUpto7z8NISZYqIO\n",
       "aTTuTTVXrRIXC1GwcTjw089L5OUb4VrURRkEBkSBIDdOKee9qq4RqKpq52wKBjF2B8bvV34PNjJR\n",
       "QT3UEGnAh31jlReeew5wONp+AwW8DveCzpw5EzNnznR7beHChfJxYmIiPv/8c89H5gs2bECkc9vR\n",
       "yZRwHLRYcZXgkIj8wty50gcMAHz+OUdNEXnJuIPVyDoh7QQ0G7T4a7gOgbPHkbzJNT4QAErOnsah\n",
       "wdEYfrweBgeAzz6Tmt1R0LrJbJcn4h0dEIVTyeGCI6JA8G5yPH5Z2wQ0NQH5+dIEuQu+h1LwYC1D\n",
       "K4w5RmSPz8aae38mv7Z5XJL0pJiIOjZqFOAqAauvB776Smw8REHiTtVuinWTUnBGy88t6h71+ECb\n",
       "zea+tX/FCnGBkU9QT/tg2Qd5SpVBD9x3n/ICd1UENSYqWlFRVYGMhX1xXbPSBHDzOI7jIuo0jca9\n",
       "qSbLP4h63dh6E0YfrQUAWAB8dEN/sQFRQNk0XnUf9M03QGWluGBIqKhGC663KF8e8ybwHpk86NFH\n",
       "AYOzZHHLFmDzZrHxkDBMVLRh7KFqRJmsAIBTSWEoHBAlOCIiP6NKVNS+/2+cOlksLhaiILDw9Hn5\n",
       "+INQLSoSw9o5m6hrziaE4cAQZ1NNmw1YvVpsQCTMpF2VcHW+2aHX4EwSyz7Ig9LTgXvuUdbPPiss\n",
       "FBKLiYo2TN55Tj5m2QdRN4wbh/IQqQ1OjM2OSc1WwQERBbBduzC5Tmr+bNMAr0ToBAdEgcitYeLK\n",
       "leICIaGMO5R75I85EY96w2OPAa4JIF9/DWzfLjYeEoJXl1bo7Q5cvVvZ0siyD6Ju0GjwlapT/OwW\n",
       "zsMm6jWu5rUANk3oi2M6JtfJ8zaPT4J8Jd+4EQkWJqCDTZ96Cy4/WC2vV4fwqwT1gksuAe64Q1mr\n",
       "PuMoePDq0orx9SbENEofvqVa4Mig6A7eQRR8XB3hs8dnw5hjbPWcDapExSyzHVobGyIRedzBg27z\n",
       "5j+4ib0pqHdUxoViV5Rzm7/djmnV9WIDIq+btOscdHbps/zAkD4oZVKUPEh9b3nPiaPKD9auBfbv\n",
       "FxcYCcFERSum1ygfvJ+FaOFg13Sii6g7wldUVbR6zp7IcFTGhgAAkhzAqKM13gyRKDi88IJ8uGV0\n",
       "Ao5nsKcS9Z7c+D7y8UwmKoLO1O1K2QenfZCnqe8tt5kbgNmzlR8+/7y4wEgIJiouZLPhetUH72rW\n",
       "3hF1m0OjcSudUvd+ISIPKCoCli+Xlx/cPEBgMBQMNsRFy327xtWbEF/TIjgi8pYkuwOjDytlH26T\n",
       "YIh6w5NPKscrVwIFBeJiIa/jt/ALff89Eq02AMD5mBD8qOduCqKeUCcqJu2qhNbO8g9Puvfee5Gc\n",
       "nIyRI0e2ec6DDz6IzMxMjBo1Cvn5+V6MjnrdSy8BdqlrwA99InD4kj4dvIGoZyoNemDKFADSTeTk\n",
       "nRxT2hmBcK2+tcUOnfMj/Hu9BpVxoWIDosB3+eXAjBnSsd0OvPii2HjIq5iouNCqVfLhd5cnwsFp\n",
       "H0Qdaq9fxf6hMaiOlgaZJdSacWlhrYAIA9fPf/5z5ObmtvnzdevW4dixYygsLMQbb7yB+++/34vR\n",
       "kae0+t9YWRnwzjvyOf/slygkNgpC8+bJh1O3nxUYiP8IhGv1XLPSFPsT7jgmb1Hvqvj3v4GSEnGx\n",
       "kFfxKqNmtwOffCIvuaWNqHPa61dh12rwnbr8YxefvnnSpEmTEBcX1+bP165di7vvvhsAMHHiRNTU\n",
       "1KCiovWeIuS7Wv1v7NVXAYtFOr7qKuxwNTkk6m1z5sijAy8rqEViNcs/OuLv1+q4WjMmW6TtFHYN\n",
       "S6PJi665Bpg8WTq2WoFXXhEbD3mNXnQAPmXrVuD0aQBATbQB+4bGCg6IKDBsvjwRszaeAiD1qdAM\n",
       "ihQcUfAoLy9HRkaGvE5PT0dZWRmSk5MvOnfx4sXysdFohNFo9EKE1C1nzwJvvKGsn3wSePo34uKh\n",
       "4NK3LzB1KvDNNwCAKTvO4YAXbinz8vKQl5fX6/8cETp7rRZ1nZ6y45z8dHPfsFicqTRhsFf+yRSs\n",
       "XDsJk+OTkffkk8DmzdIP3nwT+N3vYLx7gZy4T45PRt76PHHBksyT12kmKtTUZR9jE2HnyCUij9iT\n",
       "FYvzGiDBAfStasHIvs2iQwoqDod7XxBNGyVt6htg8nF//jPQ1CQdjxkDzJzJRAV51/z5cqLCuP0s\n",
       "/h6b2uv/yAu/mC9ZsqTX/5ne1JlrtajrtFFV4rNxQhKwjtvvqXe5dhKeWXoGmDYNGDcO2LkTaGkB\n",
       "/vQnVFRVIGVRCgBI55BP8OR1mvu2XBwOt7IPdQNAIuoZm16Lz0OUy810jrTzmrS0NJSWlsrrsrIy\n",
       "pKWlCYyIeqqP1Qb8/e/KC08+KU9hIPKa2bNhdR6OOFaHfi0WoeH4O1++VidWt2Cks7+UTQN8dznv\n",
       "kcnLNBrgd79T1q+/jhjn8AMKXExUuOzcCZw8CQCo0WmRn82yDyJPUtez5lTXS8lB6nWzZs3Ce++9\n",
       "BwDYunUrYmNjWy37IP/xk7PVQL0z2Zed7T5nnshbEhPxYx+ljC+HCege8eVr9eQd56B1fmTvyY5D\n",
       "dUyI2IDIb6gbQZeU9nAXzs03AyNGSMcNDfjp2er2zye/x9IPF1XZx7ex0bDpmcMh8qSNBg0aIvSI\n",
       "MlmRbrYA+fnA2LGiw/J7d9xxBzZt2oTKykpkZGRgyZIlsDgbLC5cuBA33HAD1q1bhyFDhiAyMhJv\n",
       "v/224IipJ8Kabbi7okp54X//V25q2F2uG0kAKCktQQpSevTnUfDIjY/GpLpGAMDMqjrB0fg2f75W\n",
       "qye75E3gbgrqPFf5BgAcf+R4z/4wrRZ44gngJz8BANxVUYUvm6wwhfPrbKDi3ywAOBwof+1vcG2w\n",
       "+8DWJDQcIn/W1pces0aDH0bHY/oPzi7mq1YxUeEBy5cv7/CcpUuXeiES8oab804h1uYcEThoEHDH\n",
       "HT3+Mz16I0lB5evYaCzWVcBgc+AyU7M0Mjc9XXRYPslfr9WJFitGHJOSUFYAm1n2QSLNmwc89RRw\n",
       "7BhibHbM+vYUPrqxv+ioqJdw2wAA7N2LtCapuV9jmA4bdNySTtRd6jGKNpt7/eAmde+XVatY/kHU\n",
       "BQaLHfO/VGrY8dhjgJ7PG0icOr0OBzNjlBd27hQXDPWKSxuV5tfb9BrURRsERkNBT6cDHn9cXt6+\n",
       "vhQhZvaqCFRMVABuZR8/jk6AmU3JiHrFzhFxaArVSYvCQuDAARhzjHL9ojHHKDQ+Il92w+bTSKg1\n",
       "S4vUVOCee4TGQwQARwdGK4tdu8QFQr3iUpOSqNit5/0xeZ+6z4UxxwjcdRfgHOUbX2fBjZtOiw2Q\n",
       "eg0TFQ6HW6Ji03huaSPqLeYQHX4cnaC8sGqVPF4qZVGKPA+biNzpHQ4sUO+meOQRIDRUXEBEToUD\n",
       "opTF7t3iAqFeMVyVqMhnooIEUO/UraiqAEJCgEcflX++4MtSGOzcoRuImKg4dAg4ehQA0BSqw/aR\n",
       "8YIDIgpsbuUfqpHARNS2O1rsSKmUvjBU6XXAL38pOCIiSYF6RwUTFQFneCMTFeSDfvELVOqlHbp9\n",
       "q1ow63yt4ICoNzBRofqitPWyeJhDdAKDIQp82y+LR5PWebNz8CAGNbWIDYjIx2ntDvy2SanBfTc5\n",
       "DoiMbOcdRN5TnhyulPSdOQOc5jZsf9RqGebZs+hnsQIAWgxaHNUxUUE+Ijwc76QoD5fvO3MesFoF\n",
       "BkS9ISgSFe3WwKvKPjaz7IOo1zWH6rBe9VRmQnFpO2cT0eSd5zDUmadoiNDjw6Q4sQERqdi1Ghzr\n",
       "z/IPf9dqGWZ+vvzzov5RsLGHG/mQ5UmxqIuUGkoPaLEAK1cKjog8LSgSFW3WwBcUAPv3AwCaNRps\n",
       "vSyhjT+BiDxpdYhys3NrM7s1E7XJ4cCdn5fIy0+vS0ODnjv/yLcUsE9FYFL9Xbr9HRP5AJNOh9XT\n",
       "VOOQn38esNvFBUQeFxSJijapyj6+i4lEcxhv/oi8YV2IFmbnrorRNgdSzzYJjojIN1255zyGlDYC\n",
       "AJpCtFg1Pb2DdxB5XwEnfwQU15SF9a+8IL/m9ndM5CNWX58Gk+v728GDwNq1YgMijwruRIWq7GND\n",
       "HC/ARN5Sr9VgxwiltnDyznMXneMq2eLIUgpaDgd++p+T8vLzqamoizYIDIioderJH6e+/ILXbT/n\n",
       "mrIwUm+RXyvkjgryQfVRBqyZmqq88Nxz0kRHCgjBm6g4cULZ0mYwIC+GF2Aib9qsmv4xecfFiQpX\n",
       "yRZHllKwuqLehOFFdQCAFgArZ2SIDYioDSWpkXDti0s1W2GuKBcaD/VcVKMFqeekiR8WnQbFaWzg\n",
       "S77p4xkZaHb1T9m5E/jqK7EBkccEb6JCPRZx+nTW/BJ52Q9jEmB1dhDPPlGP5MrmDt5BFFwWnj4v\n",
       "H78TpsX5uFCB0RC1za7TYL+qSXK2idOc/F1mSYN8fDw9ElZ98H5lIN9WHROCVUmxygvPPisuGPKo\n",
       "4L3qqMo+MHeuuDiIglRDpAG7hivTCybtunhXBVEgaXcC1YV+/BFX1JsAADatBn8KV5LprvpxlkaR\n",
       "L8lXJSqGm5h49nfqREUh+1OQj3srOR7QSxNA8N130v/I7wVdoqKkuARTRw0Btm0DAFg0wBV/fR4l\n",
       "pSUdvJOIPK2j8g+iQNLmBKrWPPecfPj1lX1RrFO+BLrqx1kaRb5kDxMVAWVocb18zP4U5OtOhxqA\n",
       "n/1MeUH1GUr+K+gSFTbYcNsI5cN0z6VxCH8oDTYbRyQSedv3YxNhdR6PPFaHvmZLu+cTBYX8fOCL\n",
       "LwAAdg3wwU0DBAdE1LHdqkTFpUxU+L3MEiVRwYkf5BcefxzQOr/arl8v9asgvxZ0iQoAmKKaMKB+\n",
       "oktE3lUXbcBmg3Jze31NQztnEwWJ55+XDzePS0JpvwiBwRB1ziGdBhbnzp/+LRagulpwRNRd0XYH\n",
       "+p+R2qNaIfWoIPIF6tLHi3bDZ2YC8+bJy6+mTXUrj+xS+SX5hKBLVKTYHRhRWAsAsEF6oktE4nwa\n",
       "olyGplfXt3MmURA4fNit2fP7N7e/m6LdmzaiXtDW75xZo8EJ9RfaPXsEREeecJlNGe94WKeBOYQN\n",
       "58k3qEsfW90N/8QT8uG0mgZElysjvrtUfkk+IegSFbe02KF1Xn83GzSo6RMiNiCiILcmVAu7c1PF\n",
       "uHoTUMEPDwpiL74oz4DPi4lEUf/2a8M7vGkj8rD2fucKB6hKBFwj4MnvjLYqiQp1k1QinzdyJL6O\n",
       "VT43f6mankX+J2ATFertPeqM/61mu3z8WUjA/usT+Y0KrQb7M2MAADoA+OwzofEQCXPiBPDBB/Ly\n",
       "n/2444/8i1vTRSYq/NYYJirIjy3rlyAf31BVBxw7JjAa6okOv6nn5uYiKysLmZmZeOmll1o9Jy8v\n",
       "D2PGjMGIESNgNBo9HWO3qLf3uDL+MXVmTLFIF1+7BljDRAWRT9g8XtUrRrXtnSiovPwy4HpCPXUq\n",
       "9kaFi42HqIvcmi7u2iUuEOqRsUxUkB87EBmOHZfGAXA+AGvj+yv5vna/qdtsNixatAi5ubk4dOgQ\n",
       "li9fjsOHD7udU1NTgwceeACff/45Dhw4gFWrVvVqwD1xze5KuKrsDg6JwWkdL75EvmDz5apExbff\n",
       "Aue5VY+CzKlTwFtvKesnnxQXC1E3FWVEwqZ13lsVFAD17Dvkb0JbbMiyKQ/19jFRQX7oA3V/p3ff\n",
       "BUpLxQVD3dZuomL79u0YMmQIBg4cCIPBgAULFmDNmjVu53z44YeYM2cO0tPTAQCJib67VXXyrkr5\n",
       "eNN4Tvsg8hWV8aE4eEkfaWGzAWvXig2IyNv++EfAbJaOJ04Err1WbDxE3WAO0aEk1TmlxuEA9u4V\n",
       "GxB12eCyRvmhXmlKBBo1TFSQ/9k7LEYuK4bFArz6qtiAqFv07f2wvLwcGRkZ8jo9PR3btm1zO6ew\n",
       "sBAWiwVTp05FfX09/ud//gd33XXXRX/W4sWL5WOj0ej1EpGoRgvGHlJGZX13eSKw4WQ77yAib9o0\n",
       "PgmXFtVJxw//N0rC7EhBitf++Xl5ecjLy/PaP49IVlkJ/POfyvp3vwP45YD8VOGAKAwua5QWu3cD\n",
       "11wjNiDqkqHFyi6YwgFRwLEagdEQdZNGg3/PGoCX/7hPWv/rX0gYmiY2JuqydhMVmk7cKFksFuze\n",
       "vRvffPMNTCYTrrzySlxxxRXIzMx0O0+dqBDhqvzz0Du3sh0aHI2zCWFC4yEid99dnohff1QEALiq\n",
       "wYQoXbuXJ4+7MIG6ZMkSr/7zKYj95S+AySQdjxoF3Hij2HiIeqBgQDRytjinN7Ghpt/JLGmQjwsG\n",
       "RjNRQX5rx4g4HIgIwwhTM9DUhLsrqvAh0kWHRV3QbulHWloaSlU1PaWlpXKJh0tGRgamT5+O8PBw\n",
       "JCQkYPLkydjrg1v9puw8Jx9vHseyDyJfcyYpHLuctbAGmwM3qCb0EAWs2lpg6VJl/cQT3E1Bfo2T\n",
       "P/xbZskFOyqI/JVG4zYB5I6zNYhqtAgMiLqq3UTFuHHjUFhYiOLiYpjNZqxYsQKzZs1yO+eWW27B\n",
       "999/D5vNBpPJhG3btmH48OG9GnRXRdsdGHegSl4zUUHkmz5VTeK5jYkKCgZ//7uUrACAYcOAOXPE\n",
       "xkPUQ8f6R0G+eh86BDQ1iQyHusBgsWOQq2wHQOGA6HbOJvJ938RGAc7vpVF2O277ulxwRNQV7SYq\n",
       "9Ho9li5dipycHAwfPhzz589HdnY2li1bhmXLlgEAsrKyMGPGDFx22WWYOHEi7rvvPp9LVNxgtiPE\n",
       "OWopX6fB6b4c+Ubkiz4NVS5J080OhDdZBUZD1MsaG4E//1lZP/44oNO1fT6RH2gK16M4LERa2GzA\n",
       "vn1iA6JOG1TeCIOzTLq8bzgaI7xbgknkaQ6NBvjf/5XXt20oQ1izTWBE1BUdXoFmzpyJmTNnur22\n",
       "cOFCt/UjjzyCRx55xLOReZD6yezq0HZzM0Qk0DGdBscyIjGktBFhACbuq8IJ0UER9ZZ//UtqpAkA\n",
       "AwYAd94pNh4iDzkUEYbBzc4pNrt3S5NsyOdlqhppFrDsgwLFggXA008Dx48jptGKWRtP4W8wiI6K\n",
       "OiHgv7WHNduQY3bIa/XWciLyPd+pSrPUvWWIAonBbgdeeUV54be/BQy8caLAcCgiVFmwT4XfUDfS\n",
       "LBzIsg8KEHo98Nhj8nJebilC7Swv9gcB/6194r7zcBV6HE+PRKGeTcqIfNkmVaJi4t7zCLPxw4QC\n",
       "z+zztcCpU9IiJQW4916xARF50KEI1WQ1Jir8BhtpUsC6+26cMUiFBAm1ZtxWWSs4IOqMgE9UqJ/I\n",
       "bmITTSKfV5IWieLUCABAuNmOa+oaO3gHkX/R2hz4xWmlwTMeeQQI48hsChyH1YmK/fsBs1lcMNQp\n",
       "ersDQ0qVz9sCNtKkQBIairdS4uXlf505D1g4AcTXBXSiIsRswxV7Oe2DyN+o/1udXl3fzplE/ue6\n",
       "rRXIMDtvkOLjgQv6PhH5uzq9Dhg8WFpYLMCBA2IDog4Nbm5BiEXawViiBeqiWYpGgeXjxFhUO3+v\n",
       "08xW4P33LzrHmGNE9vhsZI/PhjHH6OUI6UIBnagYf6Aa4S1SZ9eT/SJQnBYhOCIi6gx1omJqTQPQ\n",
       "3CwwGiLP0dgd+MkXJ5UXHnoIxjk38caIAs/Yscqxs/yDXwJ813BTi3y8h2XSFICadVqsyklXXnjh\n",
       "BWkykUpFVQVSFqUgZVEKKqoqvBwhXSigExVTdihlH5svTwQ0vPAS+YOijEgcc16doux24KuvxAZE\n",
       "5CHX7K7EwFMmaREdDSxaxBsjCkytJCr4u+67hpuUBwL5+oD+ekBBbM21aWhwjd0tLARWrRIbELUr\n",
       "YK9EBrsdV+6plNebxrPsg8hvaDT4VD1K+JNPxMVC5CkOB+5aW6KsH3gAiIsTFw9Rb2olUUG+Rb3D\n",
       "5ZJqpblgPndUUIAoKS6Rf8dLSkvQGKHH6uvTlBOefRbgBBCfFbCJiivqTYhqkrbzFGmBY/3ZvZjI\n",
       "n6xWjxJeswawWsUFQ+QB19c0IPOkNP6vSasBHn5YcEREvUidqNi7l9dwH+Ta4ZL662RcZlG+rLH0\n",
       "gwKFDTZ5F5fNWebxybR0NGqdv+MHDnBXhQ8L2ETFVapJAf8J0bLsg8jP7NZrcDY+VFrU1AC7dokN\n",
       "iKgnbDY8WK6UI36QFAf07SswIKJelpQEZGRIx83NwJEjYuOhNqWfMcH1OK8yNgRntLxnpsBVF23A\n",
       "+32VCSB4+umLelWQbwjYRMWEOpN8/G1IwP5rEgUujQb5WbHKeuNGcbEQ9dTKlchslkY0msJ0+D/V\n",
       "mDSigKXeVcFks8/KLGmQjws5lpSCwNsp8UCfPtLiyBHgww/FBkStCsxv8FVVyGqSuhfbtBps4RY2\n",
       "Ir+0J5uJCgoAViuweLG8/GRaOmoMenHxEHkL+1T4haHFyhjwggEslabAV6vXuZdfLlkijVImnxKY\n",
       "iYpNm+R/saMDo1DPLWxEfik/W9Vo8PvvAbNZXDBE3fXBB0BBAQCgIUKPlTPSO3gDUYBgosIvuO2o\n",
       "GMgdFRQkHn5YaWhdVAS8957YeOgiAZWocHUv/vev/kt+bU82O6oT+auKxDCUhRikhckE7NghNiCi\n",
       "rrJYgD/8QV5+nJOOhkiDwICIvEidqMjPh8bhEBcLtUpjdyCzRNlRUcgdFRQsYmKARx5R1s88A4Od\n",
       "1yhfElCJClf34qtDlKeubjXuROR3tkVHKAuWf5C/eecd4PhxAECNTotV07mbgoJIv35AcrJ03NiI\n",
       "AS3cFedr+lU2y1PyaqMMShNromDw4INAYqJ0XFKCOZU1YuMhNwGVqACAmDozBpdJEz+sOg0ODI0R\n",
       "HBER9cS2PkxUkJ9qaQGeeUZevpmSAFM4e1NQENFogMsvl5eXNjYLDIZa49afYmAUp+RRcImKAh5/\n",
       "XF4uPH0eBtWoXhIr4BIVo48ombDDg/ugOVQnMBoi6im3HRU//CB9+SPyB2++CZSWSsd9++LDvixF\n",
       "pCCkKv8YbuL129eo+1MUcOIHBaP77wdSUgAAKRYrbt54SnBA5BLQiYr8bJZ9EPm7syEGIDNTWjQ3\n",
       "A1u3ig2IqDOamoDnnlPWjz+OJl3AfeQSdcwtUcEdFb4ms5j9Kcj/lRSXIHt8NrLHZ6OktKRrb46I\n",
       "AJ54Ql7e+cVJhLbYPBwhdUfA3TWNOawkKvawPwVRYJg6VTlm+Qf5KFdDZ2OOEXj9deD0aQBAhUGP\n",
       "0e//s+s3T0SB4MJEBRtq+g6HA0M58YMCgA02pCxKQcqiFNhs3Ugy3HcfkC71kIqvNePWb8o9HCF1\n",
       "R0AlKhLNVgw4bQIAtAA4OKSP2ICIyDOYqCA/4GroXH/uNPDii/LryxcMQtyDqd27eSLyd/37A/Hx\n",
       "AIA+Njv6neOuCl/Rz2xFTIMFAFCjAU4lhQmOiEiQsDDgd7+Tl3esK0UEP7OF8/uuXsYcIyqqKgAA\n",
       "E0qUp1VbDRqYQ9ifgiggGI3K8dat0rb68HBh4RC15ydnq4Fz5wAAp0L0WDe5n+CIiATSaKRdFV9/\n",
       "DUDqiXC6L6/fvuBSVSnOHr2GjTQpKLm+SxrsDqzVajDQ7kBMgwU/q6gWHVrQ8/sdFa4nWCmLUjCp\n",
       "Wcl8bTL4/b8aEbmkpADZ2dKx2Sw11STyQRFNVvzXmfPy+vV+ibDw84iCnWryh3rKBIml7hmSr2eS\n",
       "goKT67tkwoP98FyE8nl9T0UVUMNxpSIF1N2TUTVOZpOBF1yigMLyD/IDczeUIdbm/CwaPBifJXBE\n",
       "NgU3Y44RD3/8b3k9tISJCl/hlqjQ8b6Z6INQLUqTpR1fMTY78Kc/CY4ouAVMoiKxqgVDnPeGLQYt\n",
       "tjMzTBRYmKggH9fHasPt68uUF55+GlYtP4souFVUVeDswgx5nVnSwIaaPsJ9R0XAfCUg6jabRoN3\n",
       "bx2ovPCXvwDnz7d5PvWugLkqjTms1BEdyIyBmXV2RIFF3adi+3agoaHNU4lEuKeiClEmq7QYNgy4\n",
       "806xARH5iNNJYWgIl/qGxdZbkFTVIjgiwunTSLJIJdNNoTocY1s3IgDAxol9cSI1QlrU1wOvvCI2\n",
       "oCAWMImK0UeUGqL8bI4lJQo4iYnAyJHSsdUKbNkiNh4KKq7Ro/L40QtVVro33lq8GNDxzp8IABxa\n",
       "DY4NUEZfZpYw0Szc7t3y4bH+UbDzAR8RAMCu1eCd2YOUF157DaioEBdQEAuYRMWYw0qiYk8WExVE\n",
       "gaKkuET+griqtkr5Acs/yIvUjZtdk6bcvPwyIu1S/WFBeCgwb56XIyTybQUDouRj9qkQx5V0/dsv\n",
       "75FfKxgY1fYbiILQd5cn4nB4qLQwmYCXXhIbUJAKiERFcmUz+lVKdXZNoTocGRTdwTuIyF/YYJO/\n",
       "IOYZVD9gooJ8xZkzwNKl8vK11ERAGxAfr0QeUzBQuTcbWswdFaK4kq5jU5TXCgbwvplIzaHV4LW0\n",
       "ROWF118HTp0SF1CQ0osOwBPU/Sn2D42BjQ2BiALSjugIac67wwHs2gXU1QF9+ogOi4KXM/tEAAAg\n",
       "AElEQVSMa5cPACTHJyMvaxTQ1ARAemr8dWz3n06q/+yS0hKkIKWDdxD5ntZ+jwtVOyoyS+qBIUmi\n",
       "wiMAmaoxseq/GyKSbIyJAsaPB3bsAJqbgeefd3soQb0vIL7Rj1aVfeSz7IMoYNXpdcDo0dLCZgO+\n",
       "+05sQBSU1Lt8cKYM+Oc/5Z+9PXuQlEzzwJ9ts9k8ES6R17X2e1yWEoFG588Ta8xINFvFBRjkYurM\n",
       "SHY2NG0xaFGSGik4IiIfpNEAf/iDsv7Xv4CTJ8XFE4T8P1HhcGCMqpHmHjbSJApsHFNKPmTh6fOA\n",
       "2QwA2BMZhq2j4gVHROSb7FoN9qpGx6tHY5J3ZZ5USm+KMiJh17GRJlGrcnKAq66Sjs1m4NlnO26u\n",
       "TR7j94mK/i0W9HVmhes0rLMjCnhMVJCPSK5sxpxKJVH+WmpSp3dTqJvElpSW9FaIRD4ln4kKnzDU\n",
       "reyD981EbdJogGeeUdZvvYWQU6XtN9cmj/H7RMWEepN8/L1ew6wwUaCbNElpVJifD1RXt38+US/5\n",
       "2ZpihDici0mT8EOfiE6/lyUeFIyYqPAN6vGw6ianRNSKa68FjEbp2GbDr09XCg0nmPh9omKiKlGR\n",
       "F+L3/zpE1JGYGODyy6VjhwPYvFlsPBSUUiuakLNF9STlmWd61JuCKBgwUeEb2EiTgl1ndjWqz5mx\n",
       "b4f8+s3n65Bx2tTqe1rjKhVhmUjX+fc3e4cDE+sb5eUmA28SiYICyz9IsLvXFENnd26nuO46YMoU\n",
       "sQER+YEjOg3MBunWM81sBSr5ZNLb+lhtSDsnJYnMAIrT2EiTgk9ndjWqz9motWDHiDgAgA7A3Z8V\n",
       "d/qf5RoJzDKRrvPLRIUrM3XDyEuQZJF+ueoj9NjHsg+i4MBEBXmBumGW+olLltWB639UbjgWlB9j\n",
       "rwmiTrBqNChKV30xzs8XF0yQylLtZDmo08Bi8MuvAkRe99Ztg+TjqdvPYmBZYztnkyd0eHXKzc1F\n",
       "VlYWMjMz8dJLL7V53o4dO6DX67F69WqPBtgaV2Zq2uV6+bW9WbGwc9stUXC45hpA7/zvf98+PpWj\n",
       "XuH6rLnwicvvTTZonZspcg0aVDw+iL0miDqpUN0TYfducYEEqeGmFvlYXYpDRO07MrgPtoxOAABo\n",
       "HcDPPz0hOKLA126iwmazYdGiRcjNzcWhQ4ewfPlyHD58uNXzHnvsMcyYMQMOh6OVP6l3jD6sdFvP\n",
       "z+JYUqKgERUFjB+vrDdtEhcLBZVLTjZgrtkur5dE6ARGQ+R/CtQ9EZio8LpLVTsqmKgg6pq3Vbsq\n",
       "Ju+qRDZ77fSqdhMV27dvx5AhQzBw4EAYDAYsWLAAa9asuei81157DXPnzkVSUlKvBXoRhwOjjyiJ\n",
       "ij3ZTFQQBRWWf5AA96jqUr8fm4jd3DZN1CVuOyp27RIXSJAazkQFUbcV9Y/C6hDlv5v/LueO3t6k\n",
       "b++H5eXlyMjIkNfp6enYtm3bReesWbMG3377LXbs2AFNG+UXixcvlo+NRiOMrjEv3TSw3IS4egsA\n",
       "oDbKgBNsBkQUXKZOBZ5/Xjr2QKIiLy8PeXl5Pf5zKHANPVGPa3YrNyVvzx4I/HWfuICI/NCJtEhY\n",
       "dRrobQ6gqAioqQFi+bDJK+rrMbDZDACwaTXYr9dgrOCQiPzNHyJ0uNVihdYBTK1tALZtAyZOFB1W\n",
       "QGo3UdFW0kHtoYcewosvvgiNRgOHw9Fm6Yc6UeEJYw5Xy8d7smLh0DIrTBRUrroKMBgAiwU4dAio\n",
       "qACSk7v9x12YQF2yZIkHgqRAoq5H3TghCcczONaPqKssBi1OpEUi82SD9MKePUAPH15RJ+3dK2+l\n",
       "LkmNQHOzRWg4RP7osF6Lbyf2xfVbz0ovPPUUsH692KACVLt7VtPS0lBaWiqvS0tLkZ6e7nbOrl27\n",
       "sGDBAgwaNAiffPIJfv3rX2Pt2rW9E62Kuuwjn2UfRMEnIgK44gplzd0Q1IsmWuy4Yl8VAMAG4J1b\n",
       "BwqNh8ifFar6VLx413wYc4ziggkmqp4g6r8DIuqa924ZCJvrGfmGDcB33wmNJ1C1m6gYN24cCgsL\n",
       "UVxcDLPZjBUrVmDWrFlu5xw/fhwnTpzAiRMnMHfuXLz++usXneNpmgv7U7CRJlFwYp8K8pKnTcpE\n",
       "j49CtTiZynJDou4qUPWpuDxDg4qqinbOJo9RJSoKBkS3cyIRtae0XwS+ujpFeeH3vwe8OFAiWLSb\n",
       "qNDr9Vi6dClycnIwfPhwzJ8/H9nZ2Vi2bBmWLVvmrRgvktXUgj6NVgDAGY20fY2IgpA6UfHtt+Li\n",
       "oIA26kgNrrNINyA2rQbPcdIHUY+oExWZJfUCIwkOxhwjssdno2DlR/Jr6r8DIuq692YNgFw8tWkT\n",
       "/t/40fLPXP/NZY/PRklpiZD4AkG7PSoAYObMmZg5c6bbawsXLmz13LffftszUXVgQp1JPt5s0AKd\n",
       "6KVBRP6vpLgE2eOzAQCny05jQGoytms0CHU4gMJCoLwcSEsTHCUFFIcDP1+t9KZYf3Uyig5Xofvd\n",
       "UIjoeHokbAB0APqfNiEi2d7RW6gHKqoqMOC+JFzyqyMAALsGKMrgrjCinjjdNxzvhmrxixbp+nXX\n",
       "kUJpV4VG2iWWskjacXH8keMiw/RrfjlXbWK9kqjYZGCSgihY2GBDyqIUpCxKQZO1CfEPpuJgVoxy\n",
       "QpCWf+Tm5iIrKwuZmZl46aWXLvp5Xl4eYmJiMGbMGIwZMwbPPvusgCj9w4VPQcYdrMaogloAgEWn\n",
       "wXu3DBQbIFEAaAnV4YhOun/TOoBhTc0dvMP/ib5ODy5rhM65M70sJQJN4R0+qySiDrwYoYPZOeZ3\n",
       "TGMTkJsrOKLA4jdXKWOOERVVFdA5HNhS1yC/nheiRV+BcRGRWHuyYjH2sLNnzcaNMP77TbneOTk+\n",
       "GXnr88QF5wU2mw2LFi3C119/jbS0NIwfPx6zZs1Cdna223lTpkzxSqNjf+f2FOQ3RW67KdZN7oeK\n",
       "xDBRoREFlHy9BpfapG/OwxsDO1HhC9dpdYlNARtpEnlEqU6D/xhTcdvX5dILTz0FzJghNqgA4jc7\n",
       "Klw3j9fcGIkYZ0b4XGwIjvnNvwER9Yb87DhlsXGjfK1IWZQSFA3atm/fjiFDhmDgwIEwGAxYsGAB\n",
       "1qxZc9F5bY2OprbNtDgw/Lh0c98M4P2bB4gNiCiA5OuVHbHDTS0CI+l9vnCdzixRHvIVspEmkcd8\n",
       "cFN/tBicX0h37gT4UMhj/GZHhcsY9bSP7DigsFpgNEQk2pHB0TBpNYiwO4ATJ5AadQmCqdq5vLwc\n",
       "GRkZ8jo9PR3btm1zO0ej0eCHH37AqFGjkJaWhldffRXDhw+/6M9avHixfGw0GmE0GnsrbN/ncODp\n",
       "RmXSx5thWlTGhwoMiCiw7HFLVHRuR0VeXh7y/HAUtS9cp4cWKzsqOJqUyHOqYkOx5tpUzFtfJr3w\n",
       "1FPQGIL34ZAnr9N+l6gYfVhJVORnxzJRQRTkrHot8qPCcbWzye6EehO2Co7JmzSdaCY8duxYlJaW\n",
       "IiIiAl9++SVuvfVWFBQUXHSe+gY42E3aVYkxzm3pzSFavByhwyWCYyIKJHt0yrVrSFML0NwMhLVf\n",
       "WnXhF/MlS5b0VngeJfo6bbDbMaisUV5z4geRZy2/sT9u/KockXYHsG8fpg9OxV70Ex2WEJ68TvtV\n",
       "4YTOasdlzqZmgFSbTkS0LVrpXj6xvrGdMwNPWloaSktL5XVpaSnS09PdzomOjkZEhDTGeebMmbBY\n",
       "LKiqqvJqnP5EY3fgns+K5fWn16WhQsvGzUSe1KDV4GRKOADnU7N9+4TG05tEX6eHNJlhcCZei7RA\n",
       "Y4TfPack8mk1fULwQV+lFHnRqUpo7cG7q8JT/CpRMay4HuEt0lbcMwmhOJ3EpmZEBGyPjpCPJ9Sb\n",
       "pPFQQWLcuHEoLCxEcXExzGYzVqxYgVmzZrmdU1FRIdc+b9++HQ6HA/Hx8SLC9QvGHecw2Pn00RSm\n",
       "w0c39BccEVFgUvdKWHz7LGSPz4YxxyguoF4i+jqtLq1Rl9wQkee8lZIAREvXtCHNZkzddlZwRP7P\n",
       "rxIVY9zKPuKATmylI6LAdyAyTP5wSDVbkXousDvIq+n1eixduhQ5OTkYPnw45s+fj+zsbCxbtgzL\n",
       "li0DAKxatQojR47E6NGj8dBDD+Gjjz4SHLXv0jncd1N8Mi0dddEGcQERBTB1r4TLB2kDtgmy6Ou0\n",
       "OlGRr/erW38iv1Gr1wEPPyyv7/msGFpb8Dw46w1+tfdrtFsjTZZ9EJHEptEAkyYB69YBkHrZnOob\n",
       "Ljgq75k5cyZmzpzp9trChQvl4wceeAAPPPCAt8PySzeer0P/01K/kxoNsHJGegfvIKLuUvdKGKqa\n",
       "ShGIRF6nuaOCyEsefhj429+AmhqkVzQhZ8sZfC86Jj/mN2lVg92OEYVKf4p89qcgIrWpU+XDMYfZ\n",
       "ZDfYGHOMyB6f3e7W8Q7PsVjwwOlKefnXcB0aIrmbgqi3qHdUDCprgN4aTDObvMRqRZZq/Gs+ExVE\n",
       "vSc2FnjkEXn5s7UlMARRObKn+U2i4rLGZoSZpQ+wY1rgXAL7UxCRpKS4BHPe+ru8Hn2kJqj6VBBQ\n",
       "UVWBlEUp7W4d7/Ccd95B/xYLAKA2Uo/XwvzmI5LILzVEGnDK2W8sxOrAgFMmwREFoMOHEeb8PKyI\n",
       "D0UlGwMT9a4HH0S1XgcASKlsxj3NTMB2l9/chU2oVz68Nhn8Jmwi8gIbbKh5dADqnZ3ME2vMyDjT\n",
       "JDgq8istLcAzz8jLFTf0Rz1v6Il6nbqh5tDieoGRBKjdu+XDQo4lJep90dH4V4rSCPfxJhsMFiYr\n",
       "usNvvvFPdEtU8OaRiNzZtRrsGxYjr9U9bYg69OabgHN8YHW0AZ9elyY4IKLgoC7/YKKiF6gTFar/\n",
       "r4mo9yxPisP5mBAAQLoduDnvlOCI/JN/JCqamzG6QXk6uinEP8ImIu/Kz1ZmWLNPBbWnpLhE7lcx\n",
       "/fpJwHPPyT/78Kb+aA7TCYyOKHioG2pmBnhDTSFUiYqCAdxRQeQNzTotPrxJGW1+5/9v797joyjv\n",
       "/YF/Zi+5kiuQhIRAAgkkEQkqiuhRQ/l5oqicqu0R9eXd6MFi1aqVWilKVcTa2tbbwXKxolKrnl/x\n",
       "tBqPekio3KKQACaBBMgdCIHcyIVkszvnj0l2ZyFsNslmn5nM5/165fXamZ1Nvg/oN8N3nuf7/L0a\n",
       "QXbOqhgsffyLf/t2BPaur6ueEIJjnI5LRP0oUjXZzWSfCvLADruzX8W8sjLg6FEAQL3Vgk/nxQuO\n",
       "jsg41E/5p9a0wcy87TsOB1BY6DzkjAoi//nvrHgcjw4EAES3dOPWBj5AGyx9FCo2b3a+5G4fRHQu\n",
       "hyeG4kRvHTO61YaU091iAyLNC+qyI+foSefx6glj0R3A2RRE/tIcHoCa3rvRoG4Hkpm3faesDGhv\n",
       "BwCcjAjAyahAwQERGYfNasJ7N0x2Ht9/rBE4xeVtg6G7QkVROgsVRNQ/2SThn6oeNuomvGQc6mUd\n",
       "59qqtM8Pv6rDuB67cpCYiI/HRXi8frA/v6qmatjfj2i0K1JtmZnRcVpgJKMM+1MQCfX5FXGo6P3X\n",
       "dnSPHXjtNbEB6Yz2CxUdHcDOnc7DIs6oICIP1LsCzWltFxgJiaJe1nGurUoBIKSzB4s+q3adWLYM\n",
       "NtPwfy2qf77dbh/29yMa7Qotrv/vMtpZqPAZdX8K7vhB5Hc9FhNWhqhmaf7mN0Azm717S/uFiq1b\n",
       "AZuyr31FQiiawwMEB0REWpZ35owKB5sXUf9+9D+1iGjvUQ6mTAHuvltoPERGVWjmjIoRwRkVRMK9\n",
       "F2hCbWywctDcDLz6qtiAdET7hQp1fwou+yCiAZSaJTSGWwEAkXYHsG+f4IhIiyIdMn78Ra3rxK9+\n",
       "BVit4gIiMjD10o+09k5kzE7zaukWeSDLZxQqOKOCSAS7JOHP/5bkOvHqq8DJk+e8nlx0Vajgsg8i\n",
       "GpAkYY86V6hyCFGfRzvtGNOhzKaoCAwAbr9dcERExnXEBGeBOUwGLvpxxIBLt+hsWdlZzv44t115\n",
       "KdDSAgBoNptQP5aNNIlE+d9LY3AwqHdVwKlTwCuviA1IJ7RdqDh1Cvj2WwCAA3D/xwcR0TkUpke5\n",
       "DliooDNMON6JhztdS4Jejx8HWCwCIyIyOEly66GQWtUmMBj9qm+sd/bHiTnimjFWHBoESJKHTxLR\n",
       "SHKYJLwRP8514o9/BA4eFBeQTmi6UPHzrMuB3kZk+ywSWsdwWi4RDcxt9lV+vjOPEJkcMpau2Y++\n",
       "1dqHJobi82hOiSYSTb00YVolt/AbLnWvj5KQIIGREBEAfBEVBsyapRx0dAB33cX70wFoulAxra7O\n",
       "+TrfwkowEXmnJi4YJyJ7p9i1tABFRWIDIs3499wazCxTpkPbTRJ+c+90VFZVcztRIsHUzR5ZqBi+\n",
       "jI4u52sWKojEkyUJWLvWNYNz2zbg5ZfFBqVxmi5UzDnV4XydZ9V0qESkJZLkPquCyz8IwLSO07jn\n",
       "vyqcxxsWTsaBKeHcTpRIA85a+iHLAqPROVnG9FOu7bm/bGHjPiJNuPBCYPly1/Hy5XyY5oF2//Xf\n",
       "0uKctmaXgG+snFFBRN5jnwpy09WFVRVHEdCj/OPnO4uE966fJDgoIupTPzYQraHKk8awjh7EneA2\n",
       "pUM1vrEL43vrPG3BZhwEt+km0oylS4E5c5TXNhtwxx3Aaea7/mi3ULFlC8y9Lw9ODkOLiYUKIvJe\n",
       "kWo747bcXMy/+iqB0ZBwy5cjrVOZCt1lNeGeMRbYLdr9FUhkOGyo6TPTVH925ZPDlCnnRKQNFgvw\n",
       "7rtAcLBy/P33wLJlYmPSKO3epamegBamc7cPIhqcI+ODUN2b4cY4HBhXy94DhvXNN27rQN/+9yko\n",
       "Y98jIs1hnwrfSFX92an/TIlInKrKKmc/rKyHH3DfovS3v1Wav5MbXRQqirgtKRENliQhX9Xb5hJV\n",
       "zxsyjhC7HbjzTud6910ZUfj/8xMER0VE/SlT7/zBGRVDpv6zU89SISJx1P2w6hvrgcWLgX/9V+VN\n",
       "WQbuvhtobRUao9Zos1DR2Ajs2QNA6cq+d1qE4ICISI/yVb1t5rBQYUgPlRwGKpQGms0SsOq+6ZC5\n",
       "lJBIk9RP/1MrT7Gh5hClVnFGBZHmSRKwbh0Q1dtTrbISeOwxoSFpjTYLFfn5zl9OB5LD0BlsERwQ\n",
       "EemRekbFhW0dQHe3wGjI3y4tOon7uly7eDwaakbDWG7TR6RVR2KC0dpbR4w6ZUOsrUdsQDoU3dyF\n",
       "cc3K77rOABNq40IER0RE55SQALz5put43Tpg0yZx8WiMNgsV6v4UXPZBRENUbZZwZLzyD9MQhwx8\n",
       "+63giMhfwk/Z8OT6A87jvIvHY2OgNn/lEZFCNkkoMrtmPPXt/kbeUzchPThpDBycQUakbYsWKV99\n",
       "cnKA48fFxaMh2rxrU/enYCNNIhoGtx433KbUGGQZP/tzGaJblKeKjREBePXOaco0SyLStEKLulDR\n",
       "JTASfVI3IWV/CiKdeOMNID5eed3QADz4IJe+QYuFioYGZZsWAN0S8H0q+1MQ0dAVpke5DlioMITb\n",
       "uhy46rsG5/HL905Ha5hVYERE5C23QkU7Z1QMlnpGRTkLFUR+o97Vo6pmkDvNRUcryz76/O1veOn8\n",
       "dN8GqEPaK1Tk5Tlf7gsNxulAs7hYiEj33GZlbdsGdPEJ3Wg2/uRp/L7d1ZfiT0Em7MwcKzAiIhqM\n",
       "Qovr1vQ8Lv0YNDbSJBJDvauH3W4f+ANnys7GB+Nd96xLSsuBqkEWPEaZAQsVubm5SEtLQ2pqKlat\n",
       "WnXW+++//z4yMzMxc+ZMXH755di7d+/wIlI98SwIYwMgIhqeE1GBqIkNVg5OnwZ27BAbEI0YySFj\n",
       "6Zr9iOidLVk3PghPhbLYTaQnZWbgdIByexpr6wGOHRMckX5E2noQd1Ipxp8GUDWB99FEevLKxBjn\n",
       "PesYh0PZstThEBuUQB4LFXa7HUuWLEFubi5KSkqwceNGlJaWul0zZcoUbNmyBXv37sWyZcvwwAMP\n",
       "DC8iVaFiJwsVROQDbrMquPxj1LrxqzpcWNoMALBLwEsPpKOdfSmIdMUhSTg4STUToLBQXDA6kJWd\n",
       "5ZxuPraq2nl+n0WC3aK9idNEdG6dZhNWPpAOe9+tS14e8PvfiwxJKI8ZrKCgACkpKUhKSoLVasWi\n",
       "RYuw6YwtU+bOnYuICKWPxJw5c1BbWzv0aI4eBfbvBwB0SxI+bW4Y4ANERANT96n49rcvIys7S1ww\n",
       "NCKmdHbhgY8OO4//smASexwR6ZRbE8jdu8UFogP1jfXO6eaZ3a7p5rstLNIS6VHp1HC8f8Nk14mn\n",
       "nwaKi8UFJJDF05t1dXVITEx0Hk+cOBE7d+485/Vr167FggUL+n3v2Wefdb7OyspCVlbW2RepnnSW\n",
       "TI9A+4kOT+EREXlFvfNH5unTaGk4etY1eXl5yFP1yCEdsdmwquIoAm3K9Mg9Zgnv3JgkNiYiGjK3\n",
       "3gosVHjtgh7XLgFFLFQQ6daGhZNx0VfHcF5Hl9Jb7Y47lKXLAQGiQ/Mrj4UKaRBTZjdv3ox169Zh\n",
       "69at/b6vLlR4+CbOl4VpkcA3LFQQ0fA1RQSg1Ayk24GAHhkXtHeedc2ZBdTnnnvOjxHSYGRlZ6G+\n",
       "sR4AEBsdi7xLr8KM3qZ73RYJ94wxI4JTnol0q3wyZ1QMxawe11r2QouEYIGxENHQ9VhMeCo5Hn8/\n",
       "eEQpVBQWAitWAM8/Lzo0v/J4J5eQkICamhrncU1NDSZOnHjWdXv37kVOTg4+/fRTREVFnfW+11SF\n",
       "Crc15UREw5RndaW7S1pZBNUz9VTnmJpK4IUXnO+tuykZxSxSEOlaZXwIuvtmBFRWAidPCo1HD0I7\n",
       "epDSW6foMUsoNnNGBZFWqbcyPddy5EPBgcDKla4TK1cC27f7J0CN8Hg3N3v2bJSXl6OyshLd3d34\n",
       "8MMPsXDhQrdrqqurcdNNN+G9995DSkrK0COpqQEOHQIAdFlNKJ0SPvTvRUR0hnxVoWLOKRYqRoPA\n",
       "LjtWHT4K9G4DtmdaBD66JnGATxGR1tktJhxOZEPNwUipbnO+rkgIRTcbCRNplnor074Zov165BGg\n",
       "b7avwwHceSfQ3u6XGLXAY6HCYrHg9ddfR3Z2NjIyMnDLLbcgPT0dq1evxurVqwEAK1asQFNTExYv\n",
       "XowLLrgAl1xyydAiUc2m+D41AjYrn4gRke9ssbpu2mZ0dAJtbR6uJj144KPDSO7qBgC0m0x4KScN\n",
       "DhNvzolGA/apGJxplaecr93+7IhIv0wm4J13gPDeB/gHDwJPPik0JH/y2KMCAK699lpce+21buce\n",
       "fPBB5+s1a9ZgzZo1w49E3Z+Cyz6IyMdOmiQcmhiKqbXtsMoAvvkGuOYa0WHREF30fSNu+qrOebwy\n",
       "MQbHxnNFNtFooez80dv4mIWKAakLFWVJYUBpo8BoiMhnJk8G/vhH4O67leO33gIWLjTEPaywaQvq\n",
       "fZ8jJ0Si7oP3ne+xUEFEI6EwQ9VDR1UcJX0J77HjqbUHXCduuAGfjONWpESjSRkbag5KapVrlqDb\n",
       "9q5EpH933gnceKPr+N57gcbRX4wUVqhQN0OL7epAQrcNANAG4AATLBGNgELVNqUsVOjXM9X1GN/U\n",
       "BQBotJiBP/0J4HpsolGlYmIobH3/W5eXAy0tQuPRsqDTdiQeU3ov2SXg8MRQwRERkU9JErB6NRAT\n",
       "oxwfPQo89JDYmPxAE40grrK5tlP6xirBzo7tRDQC9k6PgKPvxnfXLt746tFf/4obGludh8snxwGx\n",
       "sQIDIqKRYLOacDAo0HWiqEhcMBqXUtMGk6y8ro4PRVegWWxARDRs6p1BIidEIn3BlVgcbnVd8OGH\n",
       "wMaN/X5WvXLhXLuK6IEmKgJX2WTn63w20SSiEdIWakX5pN4mYw4H8M9/ig2IBufIEeA//sN5mPsv\n",
       "cfgqijPwiEarkpAg1wGXf5xTqro/BRtpEo0K6p1BOns6EbckDvufScXH6qWuDz0E1Nae9Vn1ygWP\n",
       "u4ponPiqgCy7zajIt3L6LhGNnKJ09qnQJVkG7rsPaGoCABwbG4jXbxvGlthEpHkloSxUeEPdn6Kc\n",
       "y6eJRrWViTFAUpJy0Nys9KuQZY+f0SvhhYqE+k5M7K1TtAWbUWRhoYKIRo5bs14WKjTBqymKq1cD\n",
       "ubnOw1X3p6E9ZMCNq4hIx75uaXK+Lv/4r7qfxjxSpnFGBZFhdJjNwLvvunpzffkl8OabYoMaIcIL\n",
       "FRfsb3a+3js9EnY2RCOiEbRvWgR6+g6KigzRNVnrBpyiWF4OPP648/Cd2Cj3mTFENCrtsciw994W\n",
       "TunqRlLOeF1PYx4JgQ4Hko50OI8PTmKhgmjUu+IK4IknXMdPPgkcOHDu63VKeKFiVqmrUFGUxm1J\n",
       "iWhkdQRbUNw3nViWgS1bxAZEnvX0AHfdBXT03ohnZODVhPFiYyIiv+iQJFRPCAEAmGVganXbAJ8w\n",
       "nmmdXTA7lGnfZWagM5gzzYgM4de/Bs4/X3nd2alsYdrT4/kzOiO2UCHLbjMq3KZkExGNkIKwENcB\n",
       "l39o28svA9u3AwBsEnCT3IHyuhrBQRGRv6h7Lqh7MZAio/2083WhWfjzRyLyl8BAYMMGwNq7E0hB\n",
       "AbBypdiYfExoRpt0tAPRLd0AgNZQCw4lcroaEY28nSxU6ENhIbB8ufPw3RuT0fRUEux2u8CgiMif\n",
       "ylU9F1KrTnm40pgyOlSFCvZ5Ixr11NuWZv38EWDFCtebK1YAu3aJC87HhBYqLlAt+9gzPRKyiQmW\n",
       "iEZe4ZgQwNI7PXbfPqChQWxAdLbTp4E77nBOYywKDcIH100SHBQR+VuZakbFNM6oOMt5LFQQGYp6\n",
       "29L6xnqlP8Xllytv9vQAd9yBQIfD8zfRCaGFilmqZR9FXPZBRH5SWlOD3YFW14n8fHHBUP+eeQYo\n",
       "LlZeh4RgaXI8HOazb8L7nixU1VT5OUAi8gd1c8ikunYEjJIbcJ/o7kZqZ5fzkKWoct0AABHZSURB\n",
       "VDvnERmQ2Qz8+c9AaKhyXFqKx2pHxwM4YYUKSZbdChWFbKRJRH5ihx3FP4hxneDyD23Jzwd+9zvX\n",
       "8W9+g6qggH4v7XuywOUgRKNTR7AF5b13qxa77PYPc8MrLkaA0kcTR8YHoZkzk4l0R72UY7APXZyf\n",
       "XXQ9Xpkc7zx/1/EmXFDS5OGT+iCsUJHS2YXIUzYAQIMEVCaEigqFiAzIrXkvCxWaEWq3K7t8yL13\n",
       "39nZwOLFYoMiIqEKLa7bVfVSB8Pbvdv5snxymIcLiUir1Es5BvvQRf3ZtcEm4LrrnO89tWY/Qjv0\n",
       "vQuIsELFnFOuPZ+3WCX2pyAivypOCUd33zTZ0lLg2DGxAREA4BfVx4Gq3icKUVHAunWAxN8PREam\n",
       "7r2Q0c4ZFU5uhQo2pCcyNEkC1qwBxo4FAMQ2duHh98sFBzU8wgoVl6gKFflWbqdERP7VHWBGydRw\n",
       "5/HPLr8IWdlZ4gIiXLb7BG4+2eI68dZbQHz8uT9ARIag7r2QwRkVaG9vx9dff41m1WxAddNRIjKo\n",
       "uDhg9WrnYfbWevy/Jv3uliSmQuBw4GJVoSKPhQoiEqAoPcr5et4kWemeTEJEtnbjifUHXCcWLQJu\n",
       "uUVcQESkGeoZFdM7uwCbTWA04hUWFuKRFT9BYNl+5znOqCAiAMDNN2NTtOtB3IqqY7qdNSymQrBn\n",
       "DyLtStfmkxEBOGAWEgURGVyRqonvLNV2yeRnsozH3ylDVG/fIsTHA2+8ITYmItKMJpOEo+OCAAAB\n",
       "sgyUlAiOSCxZlpEWDATblV4+R8LNaA7vv+EwERnPC5NicTw6EAAQ1WMHcnJcvb90REyhQjVVrSgt\n",
       "kuuPiUiIkqnh6Ox9nVjfiZhuYz+lE+XGky34l90nnMf3hZqRnn05l+IQkZPbjAFVbwajSm/qdL7+\n",
       "fgKLFETkcspixkv3p7lO/P3vwNq14gIaIvGFinRuS0pEYtisJmy3ugql6ia/5CeVlXi6+rjz8K0g\n",
       "Ew7/cirilsRxKQ4RObn1YNi1S1wgGpHGQgUReVCYEYVPrk5wnXjsMeDwYXEBDYH/CxU9PcCWLc7D\n",
       "wjQWKohIHHUz30tYqPCvo0eB22/HGIeyFLAmNhhPh3ItIBGdjTMq3KU1uX5ffT/BKjASItKqt388\n",
       "BYeCeguZbW3AbbcBR46IDWoQ/F+oKCwEWlsBAA1RgaiLDfZ7CEREffLVMypaWajwi85O4IUXgNRU\n",
       "YNs2AIDdJGHlA+no4FJAIupH+WTVjIqiIsBuFxeMaA4H0po5o4KIPOsOMOOp5AmAxaKc2LkTmDYN\n",
       "+PWvgQ7t3/P6tVBRX1+PQ2vWOI93T49gfwoiEuo7i4TOACUVJnbbgKoqwRGNYrIMbNwIpKUBzzwD\n",
       "tLc731p7czJKVdvFEhGpNUUEoCFKaQ6Hzk7gwAHPHxjFgmtrEdqjzEQ7ZgLqwzgTjYj691nDcayK\n",
       "i3adaG8HfvUr5V7sgw803WTTr4WKDz/+ELWfvOc8/iaRU9WISCybJOH7aRGuE6oeOuRDO3YAl12m\n",
       "TDusrnadnzED96YmYuN1k8TFRkS6UMblHwCAMWVlztdFASY+9COic7LDjtznM/Czn2dif3Cg642a\n",
       "GuD224G5c4Ht28UF6IFfCxVSTw8ubnFNVfs2JdSfP56IqF+F6VGuAxYqfKu62vWLcMcO1/nx44H/\n",
       "/E+gsBDbI/i7gIgGVs6GmgDcCxWFASxSENHACjOicHNGEvD220BMjOuNnTuVB0m33qq5WcV+LVTE\n",
       "VFcjpEeZXlJpBuqiuaaOiMQrUjf13bxZ09PgdKOtDVi2DF3JycrUwl7dkoQ1sdG4bsY04MEHXesm\n",
       "iYgGwIaaCvcZFSxUEBFQVVmF9IvTkX5xOqpq+i84OCQJyMkBysuBpUuBQNUMi7/8BaeTk7FhymTg\n",
       "1Ck/Re2ZXwsVE8sOOl/nB4jZGZWI6EwHksLQHtS7xremRnfbN2mKwwGsX680a3r+eQT27ugBAP8V\n",
       "IOHuVZfg/VUzcfjUSYFBEpEelakbahYWigtEJFlG6JlLP4jI8OywI25JHOKWxME+ULPh8HBg5Uqg\n",
       "tBT48Y+dp4NkGXdUVCv3cOvWCW9a7Nfsllhe7nydH8gKMBFpg8MsYR/7VAxffj4wezZw773K1qO9\n",
       "Dkweg0d+MQu3hltxNIY7PRHR0JyICsAJS29RWSNP/PyuogLWtjYAQEuoBVXso0lEQ5WcDPz1r7h9\n",
       "+iTsT1YVgo8dA+67T7mny8sTFp7/ChVdXZhwuMJ5mB/ICjARaQf7VAzDoUPYEjseyMpyf8oZH4+l\n",
       "SROwePlF2Ds90u0j3kxRJCJyI0koCQkSHYVYqiUv5UlhbKRJRF5T33tlZWc5z+8OC8FDyy7Eizlp\n",
       "OGZVLcktKgLmzcOXUWG4/Yo5fo/Xf9WCggJYbTYAQF1MMGrNTKxEpB1F6Wf0qaCBtbQATz4JpKfj\n",
       "yuMnnKc7TZKy9VVZGTaNi4BsOjvfD2qKIhFRLxYqVIUKdc8OIqIBqO+96hvr3d6TTRK+vDwOC2ZM\n",
       "AZ59FggJcb53dXMb1m8tAB5/HGhu9lu8/itUqG78C9MjPVxIROR/ByeNQYu5NyWqli1QP3p6gLfe\n",
       "AlJSgFdeAXqL0ADw5dxY5Zfcc88BodzNg4h8qySUhYo+bj07iIh8oNNsApYvBw4cwKax4c7zATKA\n",
       "3/1Oufd7803lXnCE+a/duqpQUZQWCZSzkRoRaYfDJOG7sBDMb24THYq2ffGFUlEvLnY7XRgajLcf\n",
       "T8f+KeHY+cROpF+cDgCoqqlCHOKG9KP6pigO9/sQ0ehREhI48EWjGWdUEJEPnOsey+28xYY7f3Uh\n",
       "frLxEM4vb1E+ePIk8JOfAG+8gZ8HmfHfJuVhVWx0LPK+yPNpjP6bUbF9u/MlZ1QQkRYVhIUMfJFR\n",
       "lZYCCxYA11zjXqSYPBn4y19wW9ok7J+iVN59tayDy0OI6Ex1AVYgKmrgC0erhgYAQJvFhCNsTkxE\n",
       "Q3Sue6wzzx+YEo6fPj0Lj06JB5KSXN+gpAQv796Hd7qOY86NYWctJfEFvzbTBIDDkQFojDR4NZyI\n",
       "NGknCxVnO3ECWLIEOP984PPPXefHjAFefFEpYNxyCxu6EZF/SBJw4YWioxBuf1RIv/1/iIh8TpLw\n",
       "RXS4cs+3ciUQ5lp2NmdfI9Yu+w7Lqo4p94w+5PetNwoSRv+a5eb9/msyohUOm0N0CH5ltL9jo4y3\n",
       "LDgQGDtWdBja0N0NvPoqkJoKvPGGay9tSVK2rCovB37xCyBYn0/0jJazAOON2Sh5q4+h/n5ZqEBp\n",
       "lD5z72AZ6r9rGC9vGW28gM7HHBQELF2q3APm5KBvHobZIeO2hmalf8Vvf6vcQ/rAgIWK3NxcpKWl\n",
       "ITU1FatWrer3mp/+9KdITU1FZmYmCtVb0/WjIGH0P7HU9X+AQyTbZNEh+JXR/o6NMl5ZkoCrrhId\n",
       "xqD5NE/LMrBpEzBjBvCzn7l1d94ZFoKbMpIR8fePkHZ9FiInROp2i1Gj5SzAeGM2St7qY6i/Xx0W\n",
       "Knx9P73fIIUKQ/13DePlLaONF9DvmPt6V0ROiET69VlIL/wn5kYHYleGaileSwvwxBNARgbwt78p\n",
       "95TD4LFQYbfbsWTJEuTm5qKkpAQbN25EaWmp2zWfffYZDh48iPLycrz99ttYvHixxx/4bfzon1FB\n",
       "RDo2b57oCAbFp3m6qAiYPx/44Q+VanmflBQ8c/EMPLr8fDQ+nojTjtOIeSgGnT2d7CFBRP6ns0LF\n",
       "SNxPl0aO/gd/RKQdfb0r1Pd+e0wynnhyJp5+ZAYqAgNcFx86BNx4I/CDHwzrZ3osVBQUFCAlJQVJ\n",
       "SUmwWq1YtGgRNm3a5HbNp59+irvuugsAMGfOHDQ3N6O+vv9mGicmxKExxH8bjRARDdowk6q/+TRP\n",
       "X3ih2w5NiIhQtqIqLsa2CeMhmU2QuCaaiERLSXFbI611vr6ftgcGoiqM/d6ISAMkCdsvGId/Oy9Z\n",
       "WTIcqdo0Iy9veN9b9uCjjz6S77//fufxhg0b5CVLlrhdc/3118tbt251Hs+fP1/+7rvv3K4BwC9+\n",
       "8YtfuvvSA+ZpfvGLX0b+0gPmaX7xi19G/hoqj9MbJC+7uMtnrD8583Nnvk9ERL7BPE1EpG3M00RE\n",
       "g+dx6UdCQgJqamqcxzU1NZg4caLHa2pra5GQkODjMImIqD/M00RE2sY8TUQ0eB4LFbNnz0Z5eTkq\n",
       "KyvR3d2NDz/8EAsXLnS7ZuHChXj33XcBADt27EBkZCRiY2NHLmIiInJiniYi0jbmaSKiwfO49MNi\n",
       "seD1119HdnY27HY77rvvPqSnp2P16tUAgAcffBALFizAZ599hpSUFISGhmL9+vV+CZyIiJiniYi0\n",
       "jnmaiGgIhtzdoh+ff/65PH36dDklJUV+6aWX+r3m4YcfllNSUuSZM2fKu3fv9uWPF2KgMb/33nvy\n",
       "zJkz5fPPP1++7LLL5D179giI0ne8+TuWZVkuKCiQzWaz/Mknn/gxOt/zZrybN2+WZ82aJZ933nny\n",
       "VVdd5d8AR8BAY25oaJCzs7PlzMxM+bzzzpPXr1/v/yB95J577pFjYmLkGTNmnPMao+UsWTbemJmn\n",
       "maf1hnnandFyliwbb8zM08zTesM87W4oOctnhYqenh556tSpckVFhdzd3S1nZmbKJSUlbtf84x//\n",
       "kK+99lpZlmV5x44d8pw5c3z144XwZszbtm2Tm5ubZVlW/oPV85i9GW/fdfPmzZOvu+46+eOPPxYQ\n",
       "qW94M96mpiY5IyNDrqmpkWVZSTp65s2Yly9fLi9dulSWZWW80dHRss1mExHusG3ZskXevXv3OROr\n",
       "EXOWEcfMPM08rSfM0+6MmLOMOGbmaeZpPWGedjfUnOWxR8Vg+HqPaD3wZsxz585FREQEAGXMtbW1\n",
       "IkL1CW/GCwCvvfYafvSjH2H8+PECovQdb8b7wQcf4Oabb3Y2xRo3bpyIUH3GmzFPmDABra2tAIDW\n",
       "1laMHTsWFovHVWSadcUVVyAqKuqc7xsxZxlxzMzT+sU8zTxtxJxlxDEzT+sX8zTz9FBzls8KFXV1\n",
       "dUhMTHQeT5w4EXV1dQNeo+dE482Y1dauXYsFCxb4I7QR4e3f8aZNm7B48WIA3m/JpUXejLe8vByN\n",
       "jY2YN28eZs+ejQ0bNvg7TJ/yZsw5OTkoLi5GfHw8MjMz8Yc//MHfYfqNEXOWEcesxjytL8zTzNNG\n",
       "zFlGHLMa87S+ME8zTw81Z/msbOOrPaL1ZDCxb968GevWrcPWrVtHMKKR5c14H330Ubz00kuQJAmy\n",
       "srTID5GNDG/Ga7PZsHv3bnz99dfo6OjA3LlzcemllyI1NdUPEfqeN2N+8cUXMWvWLOTl5eHQoUO4\n",
       "+uqrsWfPHoSFhfkhQv8zYs4y4pgB5mk9Yp7uH/P06M9ZRhwzwDytR8zT/WOeHvjPyGeFCiPuEe3N\n",
       "mAFg7969yMnJQW5ursdpMVrnzXh37dqFRYsWAQBOnDiBzz//HFar9axtuPTAm/EmJiZi3LhxCA4O\n",
       "RnBwMK688krs2bNHt4nVmzFv27YNv/zlLwEAU6dORXJyMg4cOIDZs2f7NVZ/MGLOMuKYAeZp5mn9\n",
       "YJ52Z8ScZcQxA8zTzNP6wTztbsg5a1idM1RsNps8ZcoUuaKiQu7q6hqw+c/27dt13QhHlr0bc1VV\n",
       "lTx16lR5+/btgqL0HW/Gq3b33XfrukuxN+MtLS2V58+fL/f09Mjt7e3yjBkz5OLiYkERD583Y37s\n",
       "scfkZ599VpZlWT527JickJAgnzx5UkS4PlFRUeFV8x+j5Cwjjpl5mnlaT5in3RkxZxlxzMzTzNN6\n",
       "wjztbqg5y2czKoy4R7Q3Y16xYgWampqca8ysVisKCgpEhj1k3ox3NPFmvGlpabjmmmswc+ZMmEwm\n",
       "5OTkICMjQ3DkQ+fNmJ9++mncc889yMzMhMPhwMsvv4zo6GjBkQ/Nrbfeivz8fJw4cQKJiYl47rnn\n",
       "YLPZABg3ZxlxzMzT+sU8zTxtxJxlxDEzT+sX8zTz9FBzliTLOl70RERERERERESjis92/SAiIiIi\n",
       "IiIiGi4WKoiIiIiIiIhIM1ioICIiIiIiIiLNYKGCiIiIiIiIiDSDhQoiIiIiIiIi0gwWKoiIiIiI\n",
       "iIhIM/4P0TKRLXi414gAAAAASUVORK5CYII=\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.optimize as sciOpt\n",
    "\n",
    "def F(q):\n",
    "    return 3 * q**2 - 2 * q**3\n",
    "\n",
    "def inv_cdf(y):\n",
    "    def costFunc(x): return F(x) - y\n",
    "    return sciOpt.newton(costFunc, .5)\n",
    "\n",
    "def X(q):\n",
    "    if numpy.random.uniform() <= q: return 1\n",
    "    else: return 0\n",
    "\n",
    "numsamples = 10000\n",
    "Qs = [inv_cdf(y) for y in numpy.random.uniform(size=numsamples)]\n",
    "Xs = [X(q) for q in Qs]\n",
    "Q1 = []\n",
    "Q0 = []\n",
    "for i in range(len(Xs)):\n",
    "    if Xs[i] == 1:\n",
    "        Q1.append(Qs[i]) #these are the Q values for which X=1 is observed\n",
    "    else:\n",
    "        Q0.append(Qs[i]) #these are the Q values for which X=0 is observed\n",
    "\n",
    "f,axarr = pyplot.subplots(1,3)\n",
    "f.subplots_adjust(right=2.5)\n",
    "f.subplots_adjust(top=1.5)\n",
    "\n",
    "# histogram data for PDF Q\n",
    "n, bins, patches = axarr[0].hist(Qs, 100, normed=1, facecolor='green', alpha=0.75)\n",
    "fQ = [6*(q/10.0)*(1.0-q/10.0) for q in range(11)]\n",
    "axarr[0].plot([q/10.0 for q in range(11)], fQ, color='r', lw=3)\n",
    "axarr[0].set_title(\"PDF Q\")\n",
    "axarr[0].legend([\"Theoretical\",\"Observed\"])\n",
    "\n",
    "#histogram data for PDF Q | X = 1\n",
    "n, bins, patches = axarr[1].hist(Q1, 100, normed=1, facecolor='green', alpha=0.75)\n",
    "fQ1 = [12*(q/10.0)**2*(1.0-q/10.0) for q in range(11)]\n",
    "axarr[1].plot([q/10.0 for q in range(11)], fQ1, color='r', lw=3)\n",
    "axarr[1].set_title(\"PDF Q | X = 1\")\n",
    "axarr[1].legend([\"Theoretical\",\"Observed\"])\n",
    "\n",
    "#histogram data for PDF Q | X = 1\n",
    "n, bins, patches = axarr[2].hist(Q0, 100, normed=1, facecolor='green', alpha=0.75)\n",
    "fQ0 = [12*(q/10.0)*(1.0-q/10.0)**2 for q in range(11)]\n",
    "axarr[2].plot([q/10.0 for q in range(11)], fQ0, color='r', lw=3)\n",
    "axarr[2].set_title(\"PDF Q | X = 0\")\n",
    "axarr[2].legend([\"Theoretical\",\"Observed\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
